How many questions from Properties of Solids and Liquids appear in JEE?

Properties of Solids and Liquids has appeared in 172 of the last 186 JEE Main and JEE Advanced papers — about 92% of them — contributing 344 questions in total across those papers.

Is Properties of Solids and Liquids an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 92% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Properties of Solids and Liquids questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Properties of Solids and Liquids JEE Previous Year Questions with Answers

Q1·PhysicsNumericalJEE Advanced 2026

Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates (

M_{1}

and

M_{2}

) which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area

\sqrt{10}

cm

^{2}

near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant

\epsilon_{r} = 15

and the right chamber is empty (

\epsilon_{r} = 1

). At time

t = 0

, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has

\epsilon_{r} = 1

and is maintained at atmospheric pressure. The schematic of the container at a time

t > 0

is shown in the figure. [Given: acceleration due to gravity is 10 ms

^{-2}

.] Question: The height (in m) of the liquid in left chamber at

t = 500

s is:

Q2·PhysicsSingle correctJEE Main 2026

A liquid of density 600 kg/m

^3

flowing steadily in a tube of varying cross-section. The cross-section at a point

A

is 1.0 cm

^2

and that at

B

is 20 mm

^2

. Both the points

A

and

B

are in same horizontal plane, the speed of the liquid at

A

is 10 cm/s. The difference in pressures at

A

and

B

points is ________ Pa.

(A)18
(B)144
(C)36
(D)72

Q3·PhysicsSingle correctJEE Main 2026

A spherical liquid drop of radius

R

acquires the terminal velocity

v_1

when falls through a gas of viscosity

\eta

. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity

v_2

falling through the same gas. The ratio of terminal velocities

v_1/v_2

is ________.

(A)4
(B)0.25
(C)32
(D)16

Q4·PhysicsSingle correctJEE Main 2026

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 × 10

^{8}

N/m² and its radius is 4 mm, then maximum acceleration the lift can take is ________ m/s². (take g = 10 m/s² and π = 3.14)

(A)2.56
(B)3.89
(C)4.32
(D)5.16

Q5·PhysicsSingle correctJEE Main 2026

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is ________ m.

(A)1.1
(B)2.22
(C)1.21
(D)4.44

Q6·PhysicsSingle correctJEE Main 2026

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm

^{3}

(dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is __________ cm.

(A) $120\sqrt{2}$
(B) $140\sqrt{2}$
(C) $140\sqrt{3}$
(D) $120\sqrt{3}$

Q7·PhysicsSingle correctJEE Main 2026

Figure represents the extension (

\Delta l

) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load

W

connected to the other end. If the cross-sectional area of the wire is

10^{-5}

m

^{2}

then the Young's modulus of the wire is __________ N/m

^{2}

.

(A) $1.0 \times 10^{11}$
(B) $2.0 \times 10^{10}$
(C) $1.0 \times 10^{10}$
(D) $2.0 \times 10^{11}$

Q8·PhysicsSingle correctJEE Main 2026

Two wires as shown in the figure below, made of steel and have breaking stress of

12 \times 10^{8}

N/m

^{2}

. Area of cross-section of upper wire is 0.008 cm

^{2}

and of lower wire is 0.004 cm

^{2}

. The maximum mass that can be added to pan without breaking any wire is _____ kg. (take

g = 10

m/s

^{2}

)

(A)56
(B)38
(C)96
(D)5.6

Q9·PhysicsSingle correctJEE Main 2026

The Young's modulus of steel wire of radius

r

and length

L

is

Y

. If the radius

r

and length

L

of the wire are doubled then the value of

Y

(A)increases by two times
(B)reduces by half
(C)remains unchanged
(D)becomes one fourth

Q10·PhysicsNumericalJEE Main 2026

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is

600 \times 10^{-6}

m

^{3}

. The elastic potential energy stored in the wire in stretched condition would be ________ J. (Given Young modulus of copper

= 1.1 \times 10^{11}

N/m

^{2}

)

Q11·PhysicsSingle correctJEE Main 2026

Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process is ________. (S is the surface tension of mercury).

(A)8πr²S
(B)16πr²S
(C)64πr²S
(D)4πr²S

Q12·PhysicsNumericalJEE Main 2026

A cube has side length 5 cm and modulus of rigidity

10^{5}

N/m

^{2}

. The displacement produced by a force of 10 N in the upper face of cube is _____ mm.

Q13·PhysicsSingle correctJEE Main 2026

A string

A

of length 0.314 m and Young's modulus

2 \times 10^{10}

N/m

^2

is connected to another string

B

of length and Young's modulus both twice of those of

A

. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is _____ mm. (radius of both the strings is 0.2 mm and acceleration due to gravity

= 10

m/s

^2

) (Mass of both strings is to be neglected as compared to the mass of load)

(A)3
(B)2
(C)1.9
(D)1

Q14·PhysicsSingle correctJEE Main 2026

The increase in the pressure required to decrease the volume

(\Delta V)

of water is

6.3 \times 10^{7}

N/m

^2

. The percentage decrease in the volume is _____. (Bulk modulus of water

= 2.1 \times 10^{9}

N/m

^2

.)

(A) $2\%$
(B) $3\%$
(C) $6\%$
(D) $4\%$

Q15·PhysicsNumericalJEE Main 2026

The surface tension of a soap solution is

3.5 \times 10^{-2}

N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is

\alpha \times 10^{-6}

J. The value of

\alpha

is ______.

(\pi = 22/7)

Q16·PhysicsSingle correctJEE Main 2026

A metal string

A

is suspended from a rigid support and its free end is attached to a block of mass

M

. Second block having mass

2M

is suspended at the bottom of the first block using a string

B

. The area of cross sections of strings

A

and

B

are same. The ratio of lengths of strings of

A

to

B

is 2 and the ratio of their Young's moduli

(Y_{A}/Y_{B})

is 0.5. The ratio of elongations in

A

to

B

is ______.

(A)1
(B)4
(C)8
(D)6

Q17·PhysicsSingle correctJEE Main 2026

A water spray gun is attached to a hose of cross sectional area 30 cm

^{2}

. The gun comprises of 10 perforations each of cross sectional area 15 mm

^{2}

. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

(A)100 m/s
(B)10 m/s
(C)1000 m/s
(D) $15 \times 10^{2}$ m/s

Q18·PhysicsSingle correctJEE Main 2026

The temperature of a metal strip having coefficient of linear expansion

\alpha

is increased from

T_{1}

to

T_{2}

resulting in increase of its length by

\Delta L_{1}

. The temperature is further increased from

T_{2}

to

T_{3}

such that the increase in its length is

\Delta L_{2}

. Given

T_{3} + T_{1} = 2T_{2}

and

T_{2} - T_{1} = \Delta T

, the value of

\Delta L_{2}

is ______.

(A) $\Delta L_{1}[1 + 2\alpha^{2}(\Delta T)^{2}]$
(B) $\Delta L_{1}[1 + \alpha^{2}(\Delta T)^{2}]$
(C) $\Delta L_{1}[1 + 2\alpha\Delta T]$
(D) $\Delta L_{1}[1 + \alpha\Delta T]$

Q19·PhysicsSingle correctJEE Main 2026

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is

\alpha \times 10^{-6}

J. The value of α is ________. (Take surface tension of liquid = 0.08 N/m)

(A)10
(B)7
(C)8
(D)11

Q20·PhysicsSingle correctJEE Main 2026

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m

^{3}

at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take

g = 10

m/s

^{2}

)

(A)0.88
(B)8.8
(C)88.8
(D)0.088

Q21·PhysicsNumericalJEE Main 2026

A uniform wire of length

l

of weight

w

is suspended from the roof with a weight of

W

at the other end. The stress in the wire at

\frac{l}{3}

distance from the top is

\left( \frac{W}{A} + \frac{2}{\gamma} \frac{w}{A} \right)

, where,

A

is the cross sectional area of the wire. The value of γ is ________.

Q22·PhysicsNumericalJEE Main 2026

A tub is filled with water and a wooden cube 10 cm × 10 cm × 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is ________ gram. (Take water density as 1 g/cm

^{3}

and density of wood as 0.4 g/cm

^{3}

)

Q23·PhysicsSingle correctJEE Main 2026

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is

\alpha\pi \times 10^{-4}

J. The value of

\alpha

is ______. (Take

\pi = 3.14

)

(A)0.86
(B)0.64
(C)1.92
(D)7.68

Q24·PhysicsSingle correctJEE Main 2026

10 kg of ice at −10°C is added to 100 kg of water to lower its temperature from 25°C. Consider no heat exchange to surroundings. The decrement to the temperature of water is _________ °C. (specific heat of ice = 2100 J/Kg.°C, specific heat of water = 4200 J/Kg.°C, latent heat of fusion of ice =

3.36 \times 10^{5}

J/Kg)

(A)10
(B)15
(C)6.67
(D)11.6

Q25·PhysicsSingle correctJEE Main 2026

Two wires

A

and

B

made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections

3.0 \times 10^{-5}

m

^{2}

and

4.5 \times 10^{-5}

m

^{2}

, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of

A

to that of

B

is x : 3. The value of x is ______ .

(A)1
(B)4
(C)2
(D)5

Q26·PhysicsSingle correctJEE Main 2026

Which of the following best represents the temperature versus heat supplied graph for water, in the range of −20°C to 120°C ?

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q27·PhysicsSingle correctJEE Main 2026

A cubical block of density

\rho_b = 600

kg/m

^3

floats in a liquid of density

\rho_e = 900

kg/m

^3

. If the height of block is

H = 8.0

cm then height of the submerged part is ______ cm.

(A)7.3
(B)4.3
(C)6.3
(D)5.3

Q28·PhysicsSingle correctJEE Main 2026

A brass wire of length 2m and radius 1mm at 27°C is held taut between two rigid supports. Initially it was cooled to a temperature of –43°C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is ____°C

(A)–86
(B)–71
(C)–65
(D)–80

Q29·PhysicsNumericalJEE Main 2026

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If

(15000 - x)

\mu

J of work is done in blowing it further to make its diameter 14 cm, then the value of x is ____. (

\pi = 22/7

)

Q30·PhysicsNumericalJEE Main 2026

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ cm/s.

Q31·PhysicsSingle correctJEE Main 2026

The strain-stress plot for materials A,B,C and D is shown in the figure. Which material has the largest Young's modulus ?

(A)C
(B)D
(C)A
(D)B

Q32·PhysicsSingle correctJEE Main 2026

A small metallic sphere of diameter 2 mm and density 10.5 g/cm

^{3}

is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm

^{3}

respectively. The terminal velocity attained by the sphere is ________ cm/s. (

\pi = \frac{22}{7}

and g = 10 m/s

^{2}

)

(A)2.0
(B)1.0
(C)3.0
(D)1.5

Q33·PhysicsSingle correctJEE Main 2026

Given below are two statements: Statement I : Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below.

(A)Statement I is true but Statement II is false
(B)Both Statement I and Statement II are false
(C)Both Statement I and Statement II are true
(D)Statement I is false but Statement II is true

Q34·PhysicsSingle correctJEE Main 2026

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points

A

and

F

are maintained at 100 °C and 40 °C respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperature at junction points

B

and

E

are (close to) :

(A)89 °C and 73 °C respectively
(B)80 °C and 60 °C respectively
(C)80 °C and 70 °C respectively
(D)60 °C and 45 °C respectively

Q35·PhysicsSingle correctJEE Main 2026

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1 % each, then the height of the liquid in the tube will change by _____%.

(A)–1
(B)+3
(C)–3
(D)+1

Q36·PhysicsSingle correctJEE Main 2026

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at

A

and

B

are 6

\mathrm{cm}^{2}

and 3

\mathrm{cm}^{2}

respectively. The rate of flow will be_____

\mathrm{cm}^{3}

/s. (take g = 10

\mathrm{m/s}^{2}

)

(A) $\frac{200}{\sqrt{3}}$
(B) $200\sqrt{6}$
(C) $200\sqrt{3}$
(D) $100\sqrt{3}$

Q37·PhysicsNumericalJEE Main 2026

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ________ cm/s.

Q38·PhysicsSingle correctJEE Main 2026

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27°C to 87°C. The rate of consumption of the gas is _____ g/s. (Take heat of combustion of gas =

5.0 \times 10^{4}

J/g) specific heat capacity of water = 4200 J/kg. °C

(A)2.1
(B)4.2
(C)0.42
(D)0.21

Q39·PhysicsSingle correctJEE Main 2026

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are

24 \times 10^{-6}/

°C and

1.2 \times 10^{-5}/

°C, respectively. The length of this composite rod when its temperature is raised to 100°C, is ______ cm.

(A)120.20
(B)120.15
(C)120.03
(D)120.06

Q40·PhysicsSingle correctJEE Main 2026

Surface tension of two liquids (having same densities),

T_1

and

T_2

, are measured using capillary rise method utilizing two tubes with inner radii of

r_1

and

r_2

where

r_1 > r_2

. The measured liquid heights in these tubes are

h_1

and

h_2

respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights

h_1

and

h_2

and surface tensions

T_1

and

T_2

satisfy the relation :

(A) $h_1 < h_2$ and $T_1 = T_2$
(B) $h_1 = h_2$ and $T_1 = T_2$
(C) $h_1 > h_2$ and $T_1 = T_2$
(D) $h_1 > h_2$ and $T_1 < T_2$

Q41·PhysicsNumericalJEE Advanced 2025

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures

T_{P}

and

T_{Q}

, respectively, with

T_{Q} < T_{P}

, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is

W_{0}

. Subsequently, two more plates, identical to P and Q, are introduced between P and Q, as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from P to Q (Fig. 2) in the steady state is

W_{S}

, then the ratio

\frac{W_{0}}{W_{S}}

is _____

Q42·PhysicsIntegerJEE Main 2025

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is

1\ gm/cm^3

.) The unknown mass is ___ kg.

Q43·PhysicsSingle correctJEE Main 2025

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young’s modulus. The value of Young’s modulus of the wire as per this experiment is

P\times10^{10}\ Nm^{-2}

, where the value of

P

is: (Take

g=3\pi\ m/s^2

)

(A) $5$
(B) $10$
(C) $25$
(D) $2.5$

Q44·PhysicsIntegerJEE Main 2025

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of

0.8\ cm^3

. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ___ litre. (Take 1 atm

=10^5

Pa)

Q45·PhysicsSingle correctJEE Main 2025

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass-water contact angle

\simeq 0^\circ

) with

30^\circ

inclined with vertical. The length of water risen in the capillary is __________ cm. (Take

g=9.8

m/s

^2

)

(A) $\dfrac{82}{5}$
(B) $\dfrac{57}{2}$
(C) $\dfrac{71}{5}$
(D) $\dfrac{68}{5}$

Q46·PhysicsSingle correctJEE Main 2025

Two wires A and B are made of same material having ratio of lengths

\dfrac{L_A}{L_B}=\dfrac{1}{3}

and their diameters ratio

\dfrac{d_A}{d_B}=2

. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

(A) $1:6$
(B) $1:12$
(C) $3:4$
(D) $1:3$

Q47·PhysicsIntegerJEE Main 2025

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is

1727^\circ

C and power radiated by the wire is 94.2 W. Its emissivity is

\dfrac{x}{8}

where

x=

______. (Given

\sigma=6.0\times10^{-8}

W m

^{-2}

K

^{-4}

,

\pi=3.14

and assume that the emissivity of wire material is same at all wavelength.)

Q48·PhysicsIntegerJEE Main 2025

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are:

\dfrac{L_A}{L_B}=\dfrac{1}{2}

,

\dfrac{r_A}{r_B}=2

and

\dfrac{K_A}{K_B}=\dfrac{1}{2}

. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of the rods' interface is __________ K, when equilibrium is established.

Q49·PhysicsSingle correctJEE Main 2025

Two liquids A and B have

\theta_A

and

\theta_B

as contact angles in a capillary tube. If

K=\dfrac{\cos\theta_A}{\cos\theta_B}

, then identify the correct statement:

(A) $K$ is negative, then liquid A and liquid B have convex meniscus.
(B) $K$ is negative, then liquid A and liquid B have concave meniscus.
(C) $K$ is negative, then liquid A has concave meniscus and liquid B has convex meniscus.
(D) $K$ is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

Q50·PhysicsIntegerJEE Main 2025

Two slabs with square cross section of different materials (1, 2) with equal sides (

l

) and thickness

d_1

and

d_2

such that

d_2=2d_1

and

l>d_2

. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is

\theta_2=2\theta_1

. If the shear moduli of material 1 is

4\times10^9

N/m

^2

, then shear moduli of material 2 is

x\times10^9

N/m

^2

, where value of

x

is ______.

Q51·PhysicsSingle correctJEE Main 2025

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of

10^7

N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement

\theta

of the rod axis from its original position is: (shear moduli,

G=10^{10}\ N/m^2

)

(A) $\dfrac{1}{160\pi}$
(B) $\dfrac{1}{4\pi}$
(C) $\dfrac{1}{40\pi}$
(D) $\dfrac{1}{2\pi}$

Q52·PhysicsSingle correctJEE Main 2025

Consider a rectangular sheet of solid material of length

\ell=9

cm and width

d=4

cm. The coefficient of linear expansion is

\alpha=3.1\times10^{-5}\ K^{-1}

at room temperature and one atmospheric pressure. The mass of sheet

m=0.1

kg and the specific heat capacity

C_v=900\ J\,kg^{-1}K^{-1}

. If the amount of heat supplied to the material is

8.1\times10^2

J then change in area of the rectangular sheet is:

(A) $2.0\times10^{-5}\ m^2$
(B) $2.0\times10^{-3}\ m^2$
(C) $6.0\times10^{-5}\ m^2$
(D) $4.0\times10^{-5}\ m^2$

Q53·PhysicsSingle correctJEE Main 2025

A solid steel ball of diameter 3.6 mm acquired terminal velocity

2.45\times10^{-2}

m/s while falling under gravity through an oil of density

925\,\mathrm{kg\,m^{-3}}

. Take density of steel as

7825\,\mathrm{kg\,m^{-3}}

and

g

as

9.8\,\mathrm{m/s^2}

. The viscosity of the oil in SI unit is:

(A)2.18
(B)2.38
(C)1.68
(D)1.99

Q54·PhysicsIntegerJEE Main 2025

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is

n

times the volume of the bubble B, then, the value of

n

is __________.

Q55·PhysicsSingle correctJEE Main 2025

A completely full cylindrical water tank of height 1.6 m and cross-sectional area

0.5\,\text{m}^2

has a small hole in its side at a height 90 cm from the bottom. Assume the cross-sectional area of the hole to be negligibly small compared to that of the tank. If a load of 50 kg is applied at the top surface of the water in the tank, then the velocity of the water coming out at the instant when the hole is opened is: (

g=10\,\text{m/s}^2

)

(A)3 m/s
(B)5 m/s
(C)2 m/s
(D)4 m/s

Q56·PhysicsIntegerJEE Main 2025

A steel wire of length 2 m and Young’s modulus

2.0\times10^{11}

Nm

^{-2}

is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and

10^{-3}

respectively, then the elastic potential energy density of the wire is ______

\times10^5

(in SI units).

Q57·PhysicsIntegerJEE Main 2025

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm

^2

with a hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density

1.5\times10^3

kg/m

^3

. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity

=10

m/s

^2

)

Q58·PhysicsSingle correctJEE Main 2025

Match List-I (Physical Quantity) with List-II (SI Unit). Choose the correct answer from the options given below:

List-I (Physical Quantity)	List-II (SI Unit)
A.Heat capacity of body	I. $J\,kg^{-1}$
B.Specific heat capacity of body	II. $JK^{-1}$
C.Latent heat	III. $J\,kg^{-1}K^{-1}$
D.Thermal conductivity	IV. $Jm^{-1}K^{-1}s^{-1}$

(A)(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
(B)(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
(C)(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(D)(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Q59·PhysicsIntegerJEE Main 2025

The length of a light string is 1.4 m when the tension in it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is ______ m.

Q60·PhysicsSingle correctJEE Main 2025

Two water drops each of radius

r

coalesce to form a bigger drop. If

T

is the surface tension, the surface energy released in this process is:

(A) $4\pi r^2 T\left[2-2^{2/3}\right]$
(B) $4\pi r^2 T\left[2-2^{1/3}\right]$
(C) $4\pi r^2 T\left[1+\sqrt2\right]$
(D) $4\pi r^2 T\left[\sqrt2-1\right]$

Q61·PhysicsSingle correctJEE Main 2025

The fractional compression

\left(\dfrac{\Delta V}{V}\right)

of water at the depth of 2.5 km below the sea level is ______%. Given, the Bulk modulus of water

=2\times 10^9

Nm

^{-2}

, density of water

=10^3

kg m

^{-3}

, acceleration due to gravity

=g=10

ms

^{-2}

.

(A)1.75
(B)1.0
(C)1.5
(D)1.25

Q62·PhysicsIntegerJEE Main 2025

In a hydraulic lift, the surface area of the input piston is 6 cm

^2

and that of the output piston is 1500 cm

^2

. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ.

Q63·PhysicsSingle correctJEE Main 2025

In the experiment for measurement of viscosity '

\eta

' of given liquid with a ball having radius R, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. Measurement can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of

\eta

will change. Choose the correct answer from the options given below:

(A)B, D and E only
(B)A, C and D only
(C)C, D and E only
(D)A, B and E only

Q64·PhysicsSingle correctJEE Main 2025

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m

^{-3}

)

(A)1400 cm $^3$
(B)4000 cm $^3$
(C)400 cm $^3$
(D)600 cm $^3$

Q65·PhysicsSingle correctJEE Main 2025

Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases. D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

(A)A, D, E only
(B)C, D, E only
(C)B, C, D only
(D)A, B, C only

Q66·PhysicsIntegerJEE Main 2025

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of

7\times10^6

Pa, would be ______ mm

^3

. (Given bulk modulus of copper =

1.4\times10^{11}

Nm

^{-2}

)

Q67·PhysicsSingle correctJEE Main 2025

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m

^3

. If the pressure inside the bubble is 2100 N/m

^2

greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use

g=10

m/s

^2

)

(A)0.02
(B)0.1
(C)0.25
(D)0.05

Q68·PhysicsSingle correctJEE Main 2025

The amount of work done to break a big water drop of radius ‘R’ into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be :-

(A)15 J
(B)10 J
(C)20 J
(D)5 J

Q69·PhysicsIntegerJEE Main 2025

The increase in pressure required to decrease the volume of a water sample by 0.2% is

P\times10^5\ \mathrm{Nm^{-2}}

. Bulk modulus of water is

2.15\times10^9\ \mathrm{Nm^{-2}}

. The value of P is __________.

Q70·PhysicsSingle correctJEE Main 2025

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is

P_1

. The reading of the pressure gauge falls to

P_2

when the valve is opened. The speed of water flowing in the pipe is proportional to :

(A) $\sqrt{P_1-P_2}$
(B) $(P_1-P_2)^2$
(C) $(P_1-P_2)^4$
(D) $P_1-P_2$

Q71·PhysicsSingle correctJEE Main 2025

A massless spring gets elongated by amount

x_1

under a tension of 5N. Its elongation is

x_2

under the tension of 7N. For the elongation of

(5x_1-2x_2)

, the tension in the spring will be :

(A) $15$ N
(B) $20$ N
(C) $11$ N
(D) $39$ N

Q72·PhysicsSingle correctJEE Main 2025

Given below are two statements: Statement-I : The hot water flows faster than cold water. Statement-II : Soap water has higher surface tension as compared to fresh water. In the light of the above statements, choose the correct answer from the options given below:

(A)Statement-I is false but Statement-II is true
(B)Statement-I is true but Statement-II is false
(C)Both Statement-I and Statement-II are true
(D)Both Statement-I and Statement-II are false

Q73·PhysicsIntegerJEE Main 2025

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension

0.095\ \mathrm{J/m^2}

and density

10^3\ \mathrm{kg/m^3}

. The difference between pressure inside the bubble and atmospheric pressure is __________

\mathrm{N/m^2}

. (Take

g=10\ \mathrm{m/s^2}

)

Q74·PhysicsSingle correctJEE Main 2025

The tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

(A)2 m/s
(B)4 m/s
(C)6 m/s
(D)8 m/s

Q75·PhysicsIntegerJEE Main 2025

Two soap bubbles of radius 2 cm and 4 cm are in contact with each other. The radius of curvature of the common surface, in cm, is ______.

Q76·PhysicsSingle correctJEE Main 2025

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

(A) $\frac{3}{2}Mg$
(B) $\frac{Mg}{2}$
(C) $Mg$
(D) $2Mg$

Q77·PhysicsMultiple correctJEE Advanced 2024

A table tennis ball has radius

(3/2) \times 10^{-2}m

and mass

(22/7) \times 10^{-3}kg

. It is slowly pushed down into a swimming pool to a depth of d = 0.7 m below the water surface and then released from rest. It emerges from the water surface at speed v , without getting wet, and rises up to a height H . Which of the following option(s) is(are) correct? [Given: π = 22/7, g =

10ms^{-2}

, density of water =

1 \times 10^3kgm^{-3}

, viscosity of water =

1 \times 10^{-3}Pa \cdot s

.]

(A)The work done in pushing the ball to the depth d is 0.077J .
(B)If we neglect the viscous force in water, then the speed v = 7m/s .
(C)If we neglect the viscous force in water, then the height H = 1.4m .
(D)The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is 500/9.

Q78·PhysicsNumericalJEE Advanced 2024

A spherical soap bubble inside an air chamber at pressure

P_0

=

10^5

Pa has a certain radius so that the excess pressure inside the bubble is ΔP = 144Pa. Now, the chamber pressure is reduced to

8P_0/27

so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure ΔP in both the cases to be much smaller than the chamber pressure. The new excess pressure ΔP in Pa is

Q79·PhysicsIntegerJEE Advanced 2024

Two large, identical water tanks, 1 and 2, kept on the top of a building of height

H

, are filled with water up to height

h

in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are

t_{1}

and

t_{2}

, respectively. If

H = \left(\frac{16}{9}\right)h

, then the ratio

t_{1}/t_{2}

is ______.

Q80·PhysicsSingle correctJEE Main 2024

A spherical ball of radius

1\times10^{-4}

m and density

10^{5}

kg/m

^{3}

falls freely under gravity through a distance

h

before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of

h

is approximately: (The coefficient of viscosity of water is

9.8\times10^{-6}

N s/m

^{2}

,

g=9.8

m/s

^{2}

)

(A)2296 m
(B)2249 m
(C)2518 m
(D)2396 m

Q81·PhysicsSingle correctJEE Main 2024

A sphere of relative density

\sigma

and diameter D has concentric cavity of diameter d. The ratio of

\dfrac{D}{d}

, if it just floats on water in a tank is:

(A) $\left(\dfrac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}$
(B) $\left(\dfrac{\sigma+1}{\sigma-1}\right)^{\frac{1}{3}}$
(C) $\left(\dfrac{\sigma-1}{\sigma}\right)^{\frac{1}{3}}$
(D) $\left(\dfrac{\sigma-2}{\sigma+2}\right)^{\frac{1}{3}}$

Q82·PhysicsSingle correctJEE Main 2024

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

(A)1:9
(B)1:3
(C)1:81
(D)1:27

Q83·PhysicsNumericalJEE Main 2024

A liquid column of height

0.04\,cm

balances excess pressure of soap bubble of certain radius. If density of liquid is

8\times10^3\,kg\,m^{-3}

and surface tension of soap solution is

0.28\,Nm^{-1}

, then diameter of the soap bubble is ___ cm. (if

g=10\,ms^{-2}

)

Q84·PhysicsNumericalJEE Main 2024

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ cm/s.

Q85·PhysicsSingle correctJEE Main 2024

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of kerosene oil = 0.8, specific gravity of ice = 0.9) is:

(A)8 : 9
(B)5 : 4
(C)9 : 10
(D)1 : 1

Q86·PhysicsSingle correctJEE Main 2024

Correct Bernoulli's equation is (symbols have their usual meaning):

(A) $P+mgh+\dfrac12 mv^2=$ constant
(B) $P+\rho gh+\dfrac12\rho v^2=$ constant
(C) $P+\rho gh+\rho v^2=$ constant
(D) $P+\dfrac12\rho gh+\dfrac12\rho v^2=$ constant

Q87·PhysicsNumericalJEE Main 2024

A wire of cross sectional area A, modulus of elasticity

2 \times 10^{11}

Nm

^{-2}

and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle

\theta = \frac{1}{100}

radian on the points of support. The value of A is ______

\times 10^{-4}

m

^{2}

(consider x<<L). (given :

g = 10

m/s

^{2}

)

Q88·PhysicsSingle correctJEE Main 2024

A small ball of mass

m

and density

\rho

is dropped in a viscous liquid of density

\rho_{0}

. After some time, the ball falls with constant velocity. The viscous force on the ball is:

(A) $mg\left(\tfrac{\rho_{0}}{\rho}-1\right)$
(B) $mg\left(1+\tfrac{\rho}{\rho_{0}}\right)$
(C) $mg(1-\rho\rho_{0})$
(D) $mg\left(1-\tfrac{\rho_{0}}{\rho}\right)$

Q89·PhysicsSingle correctJEE Main 2024

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given :

R

= Radius of bubble,

S

= Surface tension of bubble)

(A) $\frac{4S}{R}$
(B) $\frac{4R}{S}$
(C) $\frac{S}{R}$
(D) $\frac{2S}{R}$

Q90·PhysicsNumericalJEE Main 2024

A big drop is formed by coalescing 1000 small droplets of water. The ratio of the surface energy of 1000 droplets to that of the big drop is

\tfrac{10}{x}

. The value of

x

is _______.

Q91·PhysicsSingle correctJEE Main 2024

Match List-I (description of an elastic deformation) with List-II (corresponding modulus or quantity). Choose the correct answer from the options given below:

List-I	List-II
A.A force that restores an elastic body of unit area to its original state	I.Bulk modulus
B.Two equal and opposite forces parallel to opposite faces	II.Young's modulus
C.Forces perpendicular everywhere to the surface, per unit area, same everywhere	III.Stress
D.Two equal and opposite forces perpendicular to opposite faces	IV.Shear modulus

(A)(A)-(II), (B)-(IV), (C)-(I), (D)-(III)
(B)(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
(C)(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(D)(A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Q92·PhysicsNumericalJEE Main 2024

The density and breaking stress of a wire are

6\times10^4\ \text{kg/m}^3

and

1.2\times10^8\ \text{N/m}^2

respectively. The wire is suspended from a rigid support on a planet where the acceleration due to gravity is

\dfrac{1}{3}

of the value on the surface of earth. The maximum length of the wire without breaking is ___ m (take

g = 10\ \text{m/s}^2

).

Q93·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be

90^{\circ}

. Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. In the light of the above statements, choose the correct answer from the options given below.

(A)Statement-I is false and Statement-II is true.
(B)Both Statement-I and Statement-II are true.
(C)Both Statement-I and Statement-II are false.
(D)Statement-I is true and Statement-II is false.

Q94·PhysicsNumericalJEE Main 2024

A hydraulic press containing water has two arms with diameters 14 cm and 1.4 cm. A force of 10 N is applied on the surface of water in the thinner arm (diameter 1.4 cm). The force required to be applied on the surface of water in the thicker arm (diameter 14 cm) to maintain equilibrium of water is __________ N.

Q95·PhysicsNumericalJEE Main 2024

A soap bubble is blown to a diameter of

7\,cm

.

36960

erg of work is done in blowing it further. If surface tension of soap solution is

40\,dyne/cm

then the new radius is ___ cm. Take

\left(\pi=\dfrac{22}{7}\right)

Q96·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement I: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II: The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below:

(A)Both Statement I and Statement II are false
(B)Statement I is false but Statement II is true
(C)Statement I is true but Statement II is false
(D)Both Statement I and Statement II are true

Q97·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation

P_1-P_2=\rho g(h_2-h_1)

. Statement II: In venturi tube shown

2gh=v_1^2-v_2^2

. In the light of the above statements, choose the most appropriate answer from the options given below:

(A)Both Statement I and Statement II are correct.
(B)Statement I is incorrect but Statement II is correct.
(C)Both Statement I and Statement II are incorrect.
(D)Statement I is correct but Statement II is incorrect.

Q98·PhysicsSingle correctJEE Main 2024

On celsius scale the temperature of body increases by

40^\circ C

. The increase in temperature on Fahrenheit scale is:

(A) $70^\circ F$
(B) $68^\circ F$
(C) $72^\circ F$
(D) $75^\circ F$

Q99·PhysicsNumericalJEE Main 2024

Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is ______ N. (given, atmospheric pressure

=10^5\ \text{N/m}^2

, density of mercury

=13.6\times10^3\ \text{kg/m}^3

,

g=10\ \text{m/s}^2

,

\pi=\tfrac{22}{7}

)

Q100·PhysicsSingle correctJEE Main 2024

With rise in temperature, the Young’s modulus of elasticity:

(A)changes erratically
(B)decreases
(C)increases
(D)remains unchanged

Q101·PhysicsSingle correctJEE Main 2024

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become:

(A)100 times
(B)10 times
(C) $\dfrac{1}{100}$ th
(D) $\dfrac{1}{10}$ th

Q102·PhysicsNumericalJEE Main 2024

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be __________. [Area of cross section of wire = 0.005 cm

^2

,

Y=2\times 10^{11}

Nm

^{-2}

and

g=10

ms

^{-2}

]

Q103·PhysicsNumericalJEE Main 2024

A plane is in level flight at constant speed and each of its two wings has an area of

40\,m^2

. If the speed of the air is

180\,km/h

over the lower wing surface and

252\,km/h

over the upper wing surface, the mass of the plane is ___ kg. (Take air density to be

1\,kg\,m^{-3}

and

g=10\,m/s^2

)

Q104·PhysicsNumericalJEE Main 2024

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is

4.0\times10^{-5}

m and Young's modulus of the metal

2.0\times10^{11}

N/m

^2

. The longitudinal strain developed in the wire is

\dfrac{1}{\alpha\pi}

. The value of

\alpha

is ______. [Use

g=10\ \text{m/s}^2

]

Q105·PhysicsSingle correctJEE Main 2024

A small spherical ball of radius

r

, falling through a viscous medium of negligible density has terminal velocity

v

. Another ball of the same mass but of radius

2r

, falling through the same viscous medium will have terminal velocity:

(A) $\dfrac{v}{2}$
(B) $\dfrac{v}{4}$
(C) $4v$
(D) $2v$

Q106·PhysicsSingle correctJEE Main 2024

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q107·PhysicsNumericalJEE Main 2024

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is ______ m. (Take density of sea water =

10^3

kgm

^{-3}

, Bulk modulus of rubber =

9\times10^8

Nm

^{-2}

, and

g=10

ms

^{-2}

)

Q108·PhysicsSingle correctJEE Main 2024

Young’s modulus of material of a wire of length

L

and cross-sectional area

A

is

Y

. If the length is doubled and cross-sectional area is halved then Young’s modulus will be:

(A) $\dfrac{Y}{4}$
(B) $4Y$
(C) $Y$
(D) $2Y$

Q109·PhysicsSingle correctJEE Main 2024

A block of ice at

-10^\circ

C is slowly heated and converted to steam at

100^\circ

C. Which of the following curves represent the phenomenon qualitatively?

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q110·PhysicsNumericalJEE Main 2024

Each of three blocks

P

,

Q

and

R

shown in figure has a mass of

3\,kg

. Each of the wires

A

and

B

has cross-sectional area

0.005\,cm^2

and Young’s modulus

2\times10^{11}\,N\,m^{-2}

. Neglecting friction, the longitudinal strain on wire

B

is ___

\times10^{-4}

. (Take

g=10\,m/s^2

)

Q111·PhysicsNumericalJEE Main 2024

A big drop is formed by coalescing 1000 small identical drops of water. If

E_1

be the total surface energy of 1000 small drops of water and

E_2

be the surface energy of single big drop of water, then

E_1:E_2

is

x:1

where

x=

______.

Q112·PhysicsSingle correctJEE Main 2024

A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:

(A) $8\pi R^{2}T$
(B) $3\pi R^{2}T$
(C) $\dfrac{1}{8}\pi R^{2}T$
(D) $4\pi R^{2}T$

Q113·PhysicsNumericalJEE Main 2024

Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4 : 1 and force

F_{1}

is applied to P, an extension of

\Delta l

is produced. The force which is required to produce same extension in Q is

F_{2}

. The value of

\dfrac{F_{1}}{F_{2}}

is ___.

Q114·PhysicsSingle correctJEE Main 2024

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by

l

. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

(A)3 times
(B) $\dfrac{3}{2}$ times
(C)4 times
(D)2 times

Q115·PhysicsNumericalJEE Main 2024

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms

^{-1}

and 65 ms

^{-1}

respectively. If the wing area is 2 m

^2

the lift of the wing is ______ N. (Given density of air

=1.2

kg m

^{-3}

)

Q116·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below

(A)Both Statement I and Statement II are true
(B)Both Statement I and Statement II are false
(C)Statement I is true but Statement II is false
(D)Statement I is false but Statement II is true

Q117·PhysicsNumericalJEE Main 2024

If average depth of an ocean is 4000 m and the bulk modulus of water is

2\times 10^9

Nm

^{-2}

, then fractional compression

\dfrac{\Delta V}{V}

of water at the bottom of ocean is

\alpha\times 10^{-2}

. The value of

\alpha

is __________ (Given,

g=10

ms

^{-2}

,

\rho=1000

kg m

^{-3}

).

Q118·PhysicsSingle correctJEE Main 2024

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity. Reason (R) : The restoring force depends on the bonded inter atomic and inter molecular force of solid. In the light of the above statements, choose the correct answer from the options given below :

(A)(A) is true but (R) is false
(B)(A) is false but (R) is true
(C)Both (A) and (R) are true and (R) is the correct explanation of (A)
(D)Both (A) and (R) are true but (R) is not the correct explanation of (A)

Q119·PhysicsSingle correctJEE Main 2024

Statement (I): Viscosity of gases is greater than that of liquids. Statement (II): Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below:

(A)Statement I is correct but statement II is incorrect
(B)Statement I is incorrect but Statement II is correct
(C)Both Statement I and Statement II are incorrect
(D)Both Statement I and Statement II are correct

Q120·PhysicsNumericalJEE Main 2024

The reading of pressure metre attached with a closed pipe is

4.5\times10^5

N/m

^2

. On opening the valve, water starts flowing and the reading of pressure metre falls to

2.0\times10^5

N/m

^2

. The velocity of water is found to be

\sqrt V

m/s. The value of V is ________.

Q121·PhysicsNumericalJEE Advanced 2023

A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure

P_{a}

and its temperature becomes T = 360 K. The hot air with density

\rho

rises up a vertical chimney of diameter d = 0.1 m and height h = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density

\rho_{a}

= 1.2 kg m

^{-3}

, pressure

P_{a}

and temperature

T_{a}

= 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in

\rho

and T inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity g = 10 m s

^{-2}

and

\pi

= 3.14] Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is ________ gm s

^{-1}

.

Q122·PhysicsNumericalJEE Advanced 2023

A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure

P_{a}

and its temperature becomes T = 360 K. The hot air with density

\rho

rises up a vertical chimney of diameter d = 0.1 m and height h = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density

\rho_{a}

= 1.2 kg m

^{-3}

, pressure

P_{a}

and temperature

T_{a}

= 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in

\rho

and T inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity g = 10 m s

^{-2}

and

\pi

= 3.14] When the chimney is closed using a cap at the top, a pressure difference

\Delta

P develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of

\Delta

P is ________ N m

^{-2}

.

Q123·PhysicsSingle correctJEE Advanced 2023

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as

2.9 \times 10^{-3}

m-K and

\frac{hc}{e} = 1.24 \times 10^{-6} V - m

]

List-I	List-II
P.2000 K	1.The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function 4 eV
Q.3000 K	2.The radiation at peak wavelength is visible to human eye.
R.5000 K	3.The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction
S.10000 K	4.The power emitted per unit area is 1/16 of that emitted by a blackbody at temperature 6000 K.
	5.The radiation at peak emission wavelength can be used to image human bones.

(A)P $\rightarrow$ 3, Q $\rightarrow$ 5, R $\rightarrow$ 2, S $\rightarrow$ 3
(B)P $\rightarrow$ 3, Q $\rightarrow$ 2, R $\rightarrow$ 4, S $\rightarrow$ 1
(C)P $\rightarrow$ 3, Q $\rightarrow$ 4, R $\rightarrow$ 2, S $\rightarrow$ 1
(D)P $\rightarrow$ 1, Q $\rightarrow$ 2, R $\rightarrow$ 5, S $\rightarrow$ 3

Q124·PhysicsIntegerJEE Advanced 2023

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume

V_0

to

\frac{100}{101}V_0

with the movable piston. Considering air as an ideal gas, the height (h) of the liquid column in the capillary above the liquid level in cm is________. [Given: Surface tension of the liquid is 0.075 N m

^{-1}

, atmospheric pressure is

10^{5}

N m

^{-2}

, acceleration due to gravity (g) is 10 m s

^{-2}

, density of the liquid is

10^{3}

kg m

^{-3}

and contact angle of capillary surface with the liquid is zero]

Q125·PhysicsNumericalJEE Main 2023

There is an air bubble of radius

1.0

mm in a liquid of surface tension

0.075

Nm

^{-1}

and density

1000

kg m

^{-3}

at a depth of

10

cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is __________ Pa (

g = 10

ms

^{-2}

).

Q126·PhysicsSingle correctJEE Main 2023

A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by '

\ell

'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be :

(A) $2\ell$
(B) $\ell$
(C) $4\ell$
(D) $\ell/2$

Q127·PhysicsSingle correctJEE Main 2023

Under isothermal condition, the pressure of a gas is given by

P=aV^{-3}

, where

a

is a constant and

V

is the volume of the gas. The bulk modulus at constant temperature is equal to:

(A) $\dfrac{P}{2}$
(B) $3P$
(C) $2P$
(D) $P$

Q128·PhysicsNumericalJEE Main 2023

The elastic potential energy stored in a steel wire of length

20\,m

stretched through

2\,cm

is

80\,J

. The cross sectional area of the wire is _____

mm^{2}

. (Given,

y=2.0\times10^{11}\,Nm^{-2}

)

Q129·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A spherical body of radius

(5 \pm 0.1)

mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%. Reason R: The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below

(A)Both A and R are true but R is NOT the correct explanation of A
(B)Both A and R are true and R is the correct explanation of A
(C)A is false but R is true
(D)A is true but R is false

Q130·PhysicsSingle correctJEE Main 2023

The figure shows a liquid of given density flowing steadily in a horizontal tube of varying cross-section. Cross sectional areas at

A

is

1.5\,cm^{2}

and at

B

is

25\,mm^{2}

. If the speed of the liquid at

B

is

60\,cm/s

then

(P_{A}-P_{B})

is: (Given

P_{A}

and

P_{B}

are liquid pressures at

A

and

B

points. Density

\rho=1000\,kg\,m^{-3}

)

(A) $175\,Pa$
(B) $27\,Pa$
(C) $135\,Pa$
(D) $36\,Pa$

Q131·PhysicsNumericalJEE Main 2023

The surface tension of soap solution is

3.5\times10^{-2}

Nm

^{-1}

. The amount of work done required to increase the radius of the soap bubble from

10

cm to

20

cm is ____

\times10^{-4}

J.

Q132·PhysicsSingle correctJEE Main 2023

Eight equal drops of water are falling through air with a steady speed of

10

cm/s. If the drops coalesce, the new velocity is:

(A) $10$ cm/s
(B) $40$ cm/s
(C) $16$ cm/s
(D) $5$ cm/s

Q133·PhysicsNumericalJEE Main 2023

The length of wire becomes

l_1

and

l_2

when 100N and 120 N tensions are applied respectively. If

10 l_2 = 11 l_1

, the natural length of wire will be

\frac{1}{x} l_1

. Here the value of x is ____.

Q134·PhysicsSingle correctJEE Main 2023

Given below are two statements: Statement I: Pressure in a reservoir of water is same at all points at the same level of water. Statement II: The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below:

(A)Statement I is false but Statement II is true
(B)Both Statement I and Statement II are true
(C)Statement I is true but Statement II is false
(D)Both Statement I and Statement II are false

Q135·PhysicsNumericalJEE Main 2023

Two wires each of radius 0.2 cm and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is _________

\times10^{-6}

m. [Young's modulus for steel

=2\times10^{11}

Nm

^{-2}

and

g=10

ms

^{-2}

]

Q136·PhysicsNumericalJEE Main 2023

The figure shows a liquid being pushed out of a tube by a piston having an area of cross section

2.0

cm

^2

. The area of cross section at the outlet is

10

mm

^2

. If the piston is pushed at a speed of

4

cm s

^{-1}

, the speed of the outgoing fluid is _______ cm s

^{-1}

.

Q137·PhysicsSingle correctJEE Main 2023

Young's moduli of the materials of wires A and B are in the ratio

1:4

, while their areas of cross sections are in the ratio

1:3

. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [assume the lengths of wires A and B are the same]:

(A) $36:1$
(B) $12:1$
(C) $1:36$
(D) $1:12$

Q138·PhysicsNumericalJEE Main 2023

An air bubble of diameter

6\,\text{mm}

rises steadily through a solution of density

1750\,\text{kg/m}^{3}

at the rate of

0.35\,\text{cm/s}

. The co-efficient of viscosity of the solution (neglect density of air) is ______

\text{Pas}

(given,

g=10\,\text{ms}^{-2}

)

Q139·PhysicsSingle correctJEE Main 2023

An air bubble of volume

1\,\text{cm}^{3}

rises from the bottom of a lake

40\,\text{m}

deep to the surface at a temperature of

12^\circ\text{C}

. The atmospheric pressure is

1\times10^{5}\,\text{Pa}

, the density of water is

1000\,\text{kg/m}^{3}

and

g=10\,\text{m/s}^{2}

. There is no difference of the temperature of water at the depth of

40\,\text{m}

and on the surface. The volume of air bubble when it reaches the surface will be

(A) $5\,\text{cm}^{3}$
(B) $2\,\text{cm}^{3}$
(C) $4\,\text{cm}^{3}$
(D) $3\,\text{cm}^{3}$

Q140·PhysicsNumericalJEE Main 2023

A steel rod of length 1 m and cross sectional area

10^{-4}

m

^2

is heated from

0^{\circ}

C to

200^{\circ}

C without being allowed to extend or bend. The compressive tension produced in the rod is ____

\times10^{4}

N. (Given Young's modulus of steel

=2\times10^{11}

N/m

^2

, coefficient of linear expansion

=10^{-5}

K

^{-1}

.)

Q141·PhysicsSingle correctJEE Main 2023

A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is 250 cm

^2

. The maximum pressure the smaller piston would have to bear is [Assume

g=10

m/s

^2

]:

(A) $200\times10^{6}$ Pa
(B) $20\times10^{6}$ Pa
(C) $2\times10^{6}$ Pa
(D) $2\times10^{5}$ Pa

Q142·PhysicsSingle correctJEE Main 2023

An aluminium rod with Young's modulus

Y = 7.0 \times 10^{10}

N/m

^{2}

undergoes elastic strain of

0.04\%

. The energy per unit volume stored in the rod in SI unit is:

(A) $5600$
(B) $8400$
(C) $2800$
(D) $11200$

Q143·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. In the light of the above statements, choose the most appropriate answer from the options given below

(A)A is not correct but R is correct
(B)A is correct but R is not correct
(C)Both A and R are correct and R is the correct explanation of A
(D)Both A and R are correct but R is NOT the correct explanation of A

Q144·PhysicsNumericalJEE Main 2023

A metal block of mass

m

is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is

7\times10^5

Nm

^{-2}

. The value of mass

m

is ____ kg. (Take

g = 9.8

ms

^{-2}

and

\pi = \dfrac{22}{7}

)

Q145·PhysicsSingle correctJEE Main 2023

A small ball of mass

M

and density

\rho

is dropped in a viscous liquid of density

\rho_0

. After sometime, the ball falls with a constant velocity. What is the viscous force on the ball?

(A) $F=Mg\left(1-\dfrac{\rho_0}{\rho}\right)$
(B) $F=Mg\left(1+\dfrac{\rho_0}{\rho_0}\right)$
(C) $F=Mg\left(1+\dfrac{\rho_0}{\rho}\right)$
(D) $F=Mg(1\pm\rho\rho_0)$

Q146·PhysicsNumericalJEE Main 2023

A steel rod has a radius of

20\,mm

and a length of

2.0\,m

. A force of

62.8\,kN

stretches it along its length. Young's modulus of steel is

2.0\times10^{11}\,N/m^{2}

. The longitudinal strain produced in the wire is _____

\times 10^{-5}

.

Q147·PhysicsNumericalJEE Main 2023

The surface of water in a water tank of cross section area

750

cm

^2

on the top of a house is

h

m above the tap level. The speed of water coming out through the tap of cross section area

500

mm

^2

is

30

cm/s. At that instant,

\dfrac{dh}{dt}

is

x\times10^{-3}

m/s. The value of

x

is _________.

Q148·PhysicsSingle correctJEE Main 2023

A mercury drop of radius

10^{-3}

m is broken into

125

equal size droplets. Surface tension of mercury is

0.45

Nm

^{-1}

. The gain in surface energy is:

(A) $28\times10^{-5}$ J
(B) $17.5\times10^{-5}$ J
(C) $5\times10^{-5}$ J
(D) $2.26\times10^{-5}$ J

Q149·PhysicsNumericalJEE Main 2023

A certain pressure '

P

' is applied to

1

litre of water and

2

litre of a liquid separately. Water gets compressed to

0.01\%

whereas the liquid gets compressed to

0.03\%

. The ratio of Bulk modulus of water to that of the liquid is

\tfrac{3}{x}

. The value of

x

is _______ .

Q150·PhysicsSingle correctJEE Main 2023

The Young's modulus of a steel wire of length

6

m and cross-sectional area

3

mm

^2

, is

2\times10^{11}

N/m

^2

. The wire is suspended from its support on a given planet. A block of mass

4

kg is attached to the free end of the wire. The acceleration due to gravity on the planet is

\dfrac14

of its value on the earth. The elongation of wire is (Take

g

on the earth

=10

m/s

^2

):

(A) $0.1$ cm
(B) $0.1$ mm
(C) $1$ cm
(D) $1$ mm

Q151·PhysicsNumericalJEE Main 2023

A thin rod having a length of

1

m and area of cross-section

3 \times 10^{-6}\,\text{m}^2

is suspended vertically from one end. The rod is cooled from

210^\circ

C to

160^\circ

C. After cooling, a mass

M

is attached at the lower end of the rod such that the length of rod again becomes

1

m. Young's modulus and coefficient of linear expansion of the rod are

2 \times 10^{11}\,\text{N m}^{-2}

and

2 \times 10^{-5}\,\text{K}^{-1}

, respectively. The value of M is __________ kg. (Take

g = 10\,\text{m s}^{-2}

)

Q152·PhysicsSingle correctJEE Main 2023

For a solid rod, the Young's modulus of elasticity is

3.2\times10^{11}\,Nm^{-2}

and density is

8\times10^3

kg m

^{-3}

. The velocity of longitudinal wave in the rod will be.

(A) $145.75\times10^3~ms^{-1}$
(B) $18.96\times10^3~ms^{-1}$
(C) $3.65\times10^3~ms^{-1}$
(D) $6.32\times10^3~ms^{-1}$

Q153·PhysicsSingle correctJEE Main 2023

Under the same load, wire A having length

5.0

m and cross section

2.5\times10^{-5}~m^2

stretches uniformly by the same amount as another wire B of length

6.0

m and a cross section of

3.0\times10^{-5}~m^2

stretches. The ratio of the Young's modulus of wire A to that of wire B will be:

(A) $1:1$
(B) $1:10$
(C) $1:2$
(D) $1:4$

Q154·PhysicsSingle correctJEE Main 2023

If

1000

droplets of water of surface tension

0.07

N/m, having same radius

1

mm each, combine to from a single drop. In the process the released surface energy is- (Take

\pi=\frac{22}{7}

)

(A) $8.8 \times 10^{-5}$ J
(B) $7.92 \times 10^{-4}$ J
(C) $7.92 \times 10^{-6}$ J
(D) $9.68 \times 10^{-4}$ J

Q155·PhysicsNumericalJEE Main 2023

A faulty thermometer reads

5\,^{\circ}

C in melting ice and

95\,^{\circ}

C in steam. The correct temperature on the absolute scale will be _______ K when the faulty thermometer reads

41\,^{\circ}

C.

Q156·PhysicsSingle correctJEE Main 2023

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result the elongation in the wire is 0.2 mm. If the same force is applied to another steel wire 'B' of double the length and a diameter 2.4 times that of wire 'A', the elongation in wire 'B' will be (wires having uniform circular cross sections):

(A) $6.06\times10^{-2}$ mm
(B) $2.77\times10^{-2}$ mm
(C) $3.0\times10^{-2}$ mm
(D) $6.9\times10^{-2}$ mm

Q157·PhysicsSingle correctJEE Main 2023

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is

5

cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be _________ m

(A) $0.05$
(B) $0.10$
(C) $0.20$
(D) $0.5$

Q158·PhysicsSingle correctJEE Main 2023

Choose the correct relationship between Poisson ratio

(\sigma)

, bulk modulus (K) and modulus of rigidity

(\eta)

of a given solid object:

(A) $\sigma=\dfrac{3K+2\eta}{6K+2\eta}$
(B) $\sigma=\dfrac{3K-2\eta}{6K+2\eta}$
(C) $\sigma=\dfrac{6K+2\eta}{3K-2\eta}$
(D) $\sigma=\dfrac{6K-2\eta}{3K-2\eta}$

Q159·PhysicsSingle correctJEE Main 2023

A fully loaded boeing aircraft has a mass of

5.4\times10^5\,kg

. Its total wing area is

500\,m^2

. It is in level flight with a speed of

1080\,km/h

. If the density of air

\rho

is

1.2\,kg\,m^{-3}

, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be.

(g=10\,m/s^2)

(A) $16$
(B) $10$
(C) $8$
(D) $6$

Q160·PhysicsNumericalJEE Main 2023

A metal block of base area

0.20\,m^2

is placed on a table, as shown in figure. A liquid film of thickness

0.25\,mm

is inserted between the block and the table. The block is pushed by a horizontal force of

0.1\,N

and moves with a constant speed. If the viscosity of the liquid is

5.0\times10^{-3}\,Pl

, the speed of block is _____

\times10^{-3}\,m/s

.

Q161·PhysicsSingle correctJEE Main 2023

Heat energy of

184\,kJ

is given to ice of mass

600\,g

at

-12^\circ C

. Specific heat of ice is

2222.3\,J\,kg^{-1}\,^\circ C^{-1}

and latent heat of ice is

336\,kJ\,kg^{-1}

. A. Final temperature of system will be

0^\circ C

. B. Final temperature of the system will be greater than

0^\circ C

. C. The final system will have a mixture of ice and water in the ratio of

5:1

. D. The final system will have a mixture of ice and water in the ratio of

1:5

. E. The final system will have water only. Choose the correct answer from the options given below:

(A)A and D Only
(B)A and E Only
(C)B and C Only
(D)B and D only

Q162·PhysicsSingle correctJEE Main 2023

Surface tension of a soap bubble is

2.0 \times 10^{-2}

N m

^{-1}

. Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be: (Take

\pi = \dfrac{22}{7}

)

(A) $9.24 \times 10^{-4}$ J
(B) $5.76 \times 10^{-4}$ J
(C) $0.72 \times 10^{-4}$ J
(D) $18.48 \times 10^{-4}$ J

Q163·PhysicsSingle correctJEE Main 2023

A bowl filled with very hot soup cools from

98\,^{\circ}

C to

86\,^{\circ}

C in 2 minutes when the room temperature is

22\,^{\circ}

C. How long will it take to cool from

75\,^{\circ}

C to

69\,^{\circ}

C?

(A) $1$ minute
(B) $1.4$ minutes
(C) $0.5$ minute
(D) $2$ minutes

Q164·PhysicsNumericalJEE Main 2023

In an experiment to determine the Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of

45^{\circ}

with the load axis. The length of the wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be

x\times10^{4}\ Nm^{-2}

. The value of

x

is _______.

Q165·PhysicsNumericalJEE Main 2023

A spherical drop of liquid splits into 1000 identical spherical drops. If

u_i

is the surface energy of the original drop and

u_f

is the total surface energy of the resulting drops, then (ignoring evaporation),

\frac{u_f}{u_i} = \left(\frac{10}{x}\right)

. Then value of

x

is ______.

Q166·PhysicsNumericalJEE Main 2023

A spherical ball of radius

1

mm and density

10.5

g/cc is dropped in glycerine of coefficient of viscosity

9.8

poise and density

1.5

g/cc. Viscous force on the ball when it attains constant velocity is

3696\times10^{-x}

N. The value of

x

is _________ (Given,

g=9.8

m/s

^2

and

\pi=\dfrac{22}{7}

)

Q167·PhysicsNumericalJEE Main 2023

A hole is drilled in a metal sheet. At

27^{\circ}

C, the diameter of hole is 5 cm. When the sheet is heated to

177^{\circ}

C, the change in the diameter of hole is

d\times10^{-3}

cm. The value of

d

will be _______ if coefficient of linear expansion of the metal is

1.6\times10^{-5}/^{\circ}

C.

Q168·PhysicsSingle correctJEE Main 2023

A 100 m long wire having cross-sectional area

6.25\times10^{-4}

m

^2

and Young's modulus is

10^{10}

Nm

^{-2}

is subjected to a load of 250 N, then the elongation in the wire will be:

(A) $4\times10^{-3}$ m
(B) $6.25\times10^{-3}$ m
(C) $6.25\times10^{-6}$ m
(D) $4\times10^{-4}$ m

Q169·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Steel is used in the construction of buildings and bridges. Reason R: Steel is most elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below

(A)Both A and R are correct and R is the correct explanation of A
(B)Both A and R are correct but R is NOT the correct explanation of A
(C)A is correct but R is not correct
(D)A is not correct but R is correct

Q170·PhysicsNumericalJEE Main 2022

The velocity of a small ball of mass 0.3g and density 8g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be

x \times 10^{-4}

N, the value of x is____. [use g

= 10

m/s

^2

]

Q171·PhysicsSingle correctJEE Main 2022

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R) : Because the angle of contact between the oil/ grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below.

(A)Both (A) and (R) are true and (R) is the correct explanation of (A)
(B)Both (A) and (R) are true but (R) is not the correct explanation of (A)
(C)(A) is true but (R) is false
(D)(A) is true but (R) is true

Q172·PhysicsSingle correctJEE Main 2022

If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s modules of the material of the wire will :

(A)Remains same
(B)Become 8 times its initial value
(C)Become $\frac{1^{th}}{4}$ of its initial value
(D)Become 4 times its initial value

Q173·PhysicsNumericalJEE Main 2022

A metal wire of length 0.5 m and cross-sectional area

10^{-4}

m

^2

has breaking stress

5 \times 10^{8}

Nm

^{-2}

. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be____ ms

^{-1}

.

Q174·PhysicsNumericalJEE Main 2022

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms

^{-1}

. The area of cross-section of the wire is 2.0 mm

^2

and its Young's modulus is

1.2 \times 10^{11}

Nm

^{-2}

. The extension of the wire over its natural length due to its tension will be

x \times 10^{-5}

m. The value of x is_______.

Q175·PhysicsNumericalJEE Main 2022

A string of area of cross-section 4 mm

^2

and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is ......

\times 10^{-5}

. (Use Young's modulus

10^{11}

N/m

^2

and g = 10 m/s

^2

)

Q176·PhysicsSingle correctJEE Main 2022

A pressure-pump has a horizontal tube of cross-sectional area 10

cm^2

for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water = 1000

kg/m^3

]

(A)300 N
(B)500 N
(C)250 N
(D)400 N

Q177·PhysicsNumericalJEE Main 2022

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m

^{-3}

at the rate of 0.35 cms

^{-1}

. The coefficient of viscosity of the solution is ________ poise (in nearest integer). (the density of air is negligible).

Q178·PhysicsSingle correctJEE Main 2022

The force required to stretch a wire of cross-section 1 cm

^{2}

to double its length will be : (Given Yong's modulus of the wire = 2 × 10

^{11}

N/m

^{2}

)

(A)1 × 10 $^{7}$ N
(B)1.5 × 10 $^{7}$ N
(C)2 × 10 $^{7}$ N
(D)2.5 × 10 $^{7}$ N

Q179·PhysicsNumericalJEE Main 2022

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is…….

Q180·PhysicsNumericalJEE Main 2022

A square aluminium (shear modulus is

25 \times 10^{9}\ \mathrm{Nm}^{-2}

) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of

18.0 \times 10^{4}

N. The lower edge is riveted to the floor. The displacement of the upper edge is ____

\mu

m.

Q181·PhysicsNumericalJEE Main 2022

In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm

^{2}

) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x ×

10^{11}

Nm

^{-2}

, then the value of x is __________ .

Q182·PhysicsSingle correctJEE Main 2022

A steel wire of length 3.2 m (

Y_S

= 2.0 × 10

^{11}

Nm

^{-2}

) and a copper wire of length 4.4 M (

Y_C

= 1.1 × 10

^{11}

Nm

^{-2}

), both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be: (Given

\pi = \frac{22}{7}

)

(A)360
(B)180
(C)1080
(D)154

Q183·PhysicsSingle correctJEE Main 2022

Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. B. Two bodies P and Q having equal surface areas are maintained at temperature 10ºC and 20 ºC. The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1.15 C. A carnot Engine working between 100 K and 400 K has an efficiency of 75% D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

(A)A, B, C only
(B)A, B only
(C)A, C only
(D)B, C, D only

Q184·PhysicsSingle correctJEE Main 2022

If K

_{1}

and K

_{2}

are the thermal conductivities L

_{1}

and L

_{2}

are the lengths and A

_{1}

and A

_{2}

are the cross sectional areas of steel and copper rods respectively such that

\frac{K_{2}}{K_{1}} = 9, \frac{A_{1}}{A_{2}} = 2, \frac{L_{1}}{L_{2}} = 2

. Then, for the arrangement as shown in the figure. The value of temperature T of the steel – copper junction in the steady state will be :

(A)18ºC
(B)14 ºC
(C)45 ºC
(D)150 ºC

Q185·PhysicsNumericalJEE Main 2022

A uniform heavy rod of mass 20 kg. Cross sectional area 0.4 m

^2

and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is

x \times 10^{-9}

m. The value of x is_____. :(Given. Young's modulus Y=

2 \times 10^{11}

Nm

^{-2}

and g=10 ms

^{-2}

)

Q186·PhysicsSingle correctJEE Main 2022

A water drop of radius 1cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be : [Given π = 3.14]

(A)8.5 × 10 $^{-4}$ J
(B)8.2 × 10 $^{-4}$ J
(C)7.5 × 10 $^{-4}$ J
(D)5.3 × 10 $^{-4}$ J

Q187·PhysicsSingle correctJEE Main 2022

The area of cross section of the rope used to lift a load by a crane is

2.5 \times 10^{-4}

m

^2

. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be : (take g =10 ms

^{-2}

)

(A) $6.25 \times 10^{-4}$ m $^2$
(B) $10 \times 10^{-4}$ m $^2$
(C) $1 \times 10^{-4}$ m $^2$
(D) $1.67 \times 10^{-4}$ m $^2$

Q188·PhysicsSingle correctJEE Main 2022

An ice cube of dimensions 60 cm

\times

50 cm

\times

20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at

0^\circ

C of temperature is brought to a room of temperature

40^\circ

C. The rate of melting of ice is approximately: (Latent heat of fusion of ice is

3.4 \times 10^{5}

J

\text{kg}^{-1}

and thermal conducting of insulation wall is

0.05\ \text{Wm}^{-1}{}^{\circ}\text{C}^{-1}

)

(A) $61 \times 10^{-1}\ \text{kg s}^{-1}$
(B) $61 \times 10^{-5}\ \text{kg s}^{-1}$
(C) $208\ \text{kg s}^{-1}$
(D) $30 \times 10^{-5}\ \text{kg s}^{-1}$

Q189·PhysicsNumericalJEE Main 2022

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is _______ cm.

Q190·PhysicsNumericalJEE Main 2022

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be _______ cm. (

\alpha_{iron} = 1.2 \times 10^{-5}

K^{-1}

and

\alpha_{brass} = 1.8 \times 10^{-5}

K^{-1}

).

Q191·PhysicsSingle correctJEE Main 2022

A wire of length L is hanging from a fixed support. The length changes to

L_1

and

L_2

when masses 1kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

(A) $\sqrt{L_1L_2}$
(B) $\frac{L_1+L_2}{2}$
(C) $2L_1 - L_2$
(D) $3L_1 - 2L_2$

Q192·PhysicsNumericalJEE Main 2022

A small spherical ball of radius 0.1 mm and density

10^4

kg m

^{-3}

falls freely under gravity through a a distance h before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h wil be______m. (Given g = 10 ms

^{-2}

, viscosity of water =

1.0 \times 10^{-5}

N-sm

^{-2}

).

Q193·PhysicsNumericalJEE Main 2022

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm

^2

for each plate. The equivalent thermal conductivity of the compound plate is

\left(1+\frac{5}{\alpha}\right)

K, then the value of α will be __________.

Q194·PhysicsSingle correctJEE Main 2022

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27ºC). (Given: coefficient of linear thermal expansion of gold

\alpha_\mathrm{L} = 1.4 \times 10^{-5}\ \mathrm{K}^{-1}

)

(A)125.7ºC
(B)91.7ºC
(C)425.7º
(D)152.7ºC

Q195·PhysicsSingle correctJEE Main 2022

A water drop of radius 1μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is

1.8\times10^{-5}

Nsm

^{-2}

and its density is negligible as compared to that of water

10^6

gm

^{-3}

. Terminal velocity of the water drop is: (Take acceleration due to gravity = 10 ms

^{-2}

)

(A) $145.4\times10^{-6}$ ms $^{-1}$
(B) $118.0\times10^{-6}$ ms $^{-1}$
(C) $132.6\times10^{-6}$ ms $^{-1}$
(D) $123.4\times10^{-6}$ ms $^{-1}$

Q196·PhysicsNumericalJEE Main 2022

A liquid of density 750 kgm

^{-3}

flows smoothly through a horizontal pipe that tapers in cross–sectional area from

A_1 = 1.2\times10^{-2}\,m^{2}

to

A_2 = \frac{A_1}{2}

. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ______

\times10^{-3}\,m^{3}s^{-1}

.

Q197·PhysicsSingle correctJEE Main 2022

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is: (Given, initial temperature of the bullet =

127^{\circ}

C, Melting point of the bullet =

327^{\circ}

C, Latent heat of fusion of lead =

2.5\times10^{4}

J Kg

^{-1}

, Specific heat capacity of lead = 125J/kg K)

(A) $125$ ms $^{-1}$
(B) $500$ ms $^{-1}$
(C) $250$ ms $^{-1}$
(D) $600$ ms $^{-1}$

Q198·PhysicsSingle correctJEE Main 2022

The velocity of a small ball of mass 'm' and density

d_{1}

, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is

d_{2}

, then the viscous force acting on the ball, will be :

(A) $mg\left(1-\frac{d_{1}}{d_{2}}\right)$
(B) $mg\left(1-\frac{d_{2}}{d_{1}}\right)$
(C) $mg\left(\frac{d_{1}}{d_{2}}-1\right)$
(D) $mg\left(\frac{d_{2}}{d_{1}}-1\right)$

Q199·PhysicsNumericalJEE Main 2022

The area of cross-section of a large tank is 0.5

m^{2}

. It has a narrow opening near the bottom having area of cross-section 1

cm^{2}

. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ________

cms^{-1}

. [Take g = 10

ms^{-2}

]

Q200·PhysicsNumericalJEE Main 2022

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of 5 ×

10^{-4}

is .............

kJ/m^{3}

. Assume that material is elastic upto the linear strain of 5 ×

10^{-4}

.

Q201·PhysicsSingle correctJEE Main 2022

If ρ is the density and η is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number

R_e

is :

(A) $R_e = \frac{\eta d}{\rho v}$
(B) $R_e = \frac{\rho v}{\eta d}$
(C) $R_e = \frac{\rho v d}{\eta}$
(D) $R_e = \frac{\eta}{\rho v d}$

Q202·PhysicsNumericalJEE Main 2022

A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If geyser operates on a gas burner, the rate of combustion of fuel will be _____________g min

^{-1}

[Heat of combustion = 8 ×

10^{3}

Jg

^{-1}

Specific heat of water = 4.2 Jg

^{-1}

°C

^{-1}

]

Q203·PhysicsNumericalJEE Main 2022

The elongation of a wire on the surface of the earth is

10^{-4}

m. The same wire of same dimensions is elongated by 6 ×

10^{-5}

m on another planet. The acceleration due to gravity on the planet will be ............

ms^{-2}

. (Take acceleration due to gravity on the surface of earth = 10

m/s^{-2}

)

Q204·PhysicsNumericalJEE Main 2022

An ideal fluid of density 800

kgm^{-3}

, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to

\frac{a}{2}

. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is

\frac{\sqrt{x}}{6}

ms^{-1}

for x = .................. (Given g = 10

m^{-2}

)

Q205·PhysicsSingle correctJEE Main 2022

A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper:

0.39\,\mathrm{J}\,\mathrm{g}^{-1}\,{}^\circ\mathrm{C}^{-1}

and latent heat of fusion of water : 335 J

\mathrm{g}^{-1}

]

(A)1.5 kg
(B)5.8 kg
(C)2.9 kg
(D)3.8 kg

Q206·PhysicsNumericalJEE Main 2022

A steam engine intakes 50g of steam at 100°C per minute and cools it down to 20°C. If latent heat of vaporization of steam is

540\ \mathrm{cal\ g}^{-1}

, then the heat rejected by the steam engine per minute is ______

\times 10^{3}

cal.

Q207·PhysicsNumericalJEE Main 2022

The velocity of upper layer of water in a river is

36\ \mathrm{kmh}^{-1}

. Shearing stress between horizontal layers of water is

10^{-3}\ \mathrm{Nm}^{-2}

. Depth of the river is __________ m. (Co-efficiency of viscosity of water is

10^{-2}

Pa.s)

Q208·PhysicsSingle correctJEE Main 2022

The terminal velocity

(v_t)

of the spherical rain drop depends on the radius (r) of the spherical rain drop as:-

(A) $r^{1/2}$
(B)r
(C) $r^2$
(D) $r^3$

Q209·PhysicsSingle correctJEE Main 2022

A solid metallic cube having total surface area 24

m^2

is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube

\left(\text{Given} : \alpha = 5.0 \times 10^{-4}\ {}^\circ C^{-1}\right)

(A) $2.4 \times 10^6$ cm $^3$
(B) $1.2 \times 10^5$ cm $^3$
(C) $6.0 \times 10^4$ cm $^3$
(D) $4.8 \times 10^5$ cm $^3$

Q210·PhysicsNumericalJEE Main 2022

In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference (

\Delta

T) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as

80^\circ

C. The value of t

_2

as mentioned in the graph will be ______.

Q211·PhysicsSingle correctJEE Main 2022

Two metallic blocks

M_{1}

and

M_{2}

of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of

M_{2}

is K then the thermal conductivity of

M_{1}

will be : [Assume steady state heat conduction]

(A)10 K
(B)8 K
(C)12.5 K
(D)2 K

Q212·PhysicsSingle correctJEE Main 2022

The bulk modulus of a liquid is

3\times10^{10}

Nm

^{-2}

. The pressure required to reduce the volume of liquid by 2% is :

(A) $3\times10^{8}$ Nm $^{-2}$
(B) $9\times10^{8}$ Nm $^{-2}$
(C) $6\times10^{8}$ Nm $^{-2}$
(D) $12\times10^{8}$ Nm $^{-2}$

Q213·PhysicsNumericalJEE Advanced 2021

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmospheric pressure

p_0 = 10^5

Pa so that the volume of the trapped air is

v_0

= 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure

P_0 + \Delta p

without changing its orientation. At this pressure, the volume of the trapped air is

v_0 - \Delta v

. Let

\Delta v = X

cc and

\Delta p = Y \times 10^3

Pa. The value of

X

is ____.

Q214·PhysicsIntegerJEE Advanced 2021

A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t =

t_1

and 50 K at t =

t_2

. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio

(t_2/t_1)

is_____.

Q215·PhysicsMultiple correctJEE Advanced 2021

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration

a

along a fixed inclined plane with angle

\theta = 45^\circ

.

P_1

and

P_2

are pressures at points 1 and 2, respectively, located at the base of the tube. Let

\beta = (P_1 - P_2)/(\rho g d)

, where

\rho

is density of water,

d

is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct ?

(A) $\beta = 0$ when $a = g/\sqrt{2}$
(B) $\beta > 0$ when $a = g/\sqrt{2}$
(C) $\beta = \frac{\sqrt{2}-1}{\sqrt{2}}$ when $a = g/2$
(D) $\beta = \frac{1}{\sqrt{2}}$ when $a = g/2$

Q216·PhysicsSingle correctJEE Main 2021

Due to cold weather a 1 m water pipe of cross–sectional area 1 cm

^{2}

is filled with ice at −10°C. Resistive heating is used to melt the ice. Current of 0.5 A is passed through 4 kΩ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (Given latent heat of fusion for water/ice = 3.33 × 10

^{5}

J kg

^{-1}

, specific heat of ice = 2 × 10

^{3}

J kg

^{-1}

and density of ice = 10

^{3}

kg / m

^{3}

(A)0.353 s
(B)35.3 s
(C)3.53 s
(D)70.6 s

Q217·PhysicsNumericalJEE Main 2021

A steel rod with y = 2.0 × 10

^{11}

Nm

^{-2}

and α = 10

^{-5}

°C

^{-1}

of length 4 m and area of cross-section 10 cm

^{2}

is heated from 0° C to 400°C without being allowed to extend. The tension produced in the rod is x × 10

^{5}

N where the value of x is ..........

Q218·PhysicsSingle correctJEE Main 2021

Two thin metallic spherical shells of radii

r_1

and

r_2

(r_1 < r_2)

are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature

\theta_1

and the outer shell at temperature

\theta_2 (\theta_1 < \theta_2)

. The rate at which heat flows radially through the material is :-

(A) $\frac{4\pi K r_1 r_2 (\theta_2 - \theta_1)}{r_2 - r_1}$
(B) $\frac{\pi r_1 r_2 (\theta_2 - \theta_1)}{r_2 - r_1}$
(C) $\frac{K(\theta_2 - \theta_1)}{r_2 - r_1}$
(D) $\frac{K(\theta_2 - \theta_1)(r_2 - r_1)}{4\pi r_1 r_2}$

Q219·PhysicsSingle correctJEE Main 2021

Four identical hollow cylindrical columns of mild steel support a big structure of mass

50 \times 10^3

kg, The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use

Y = 2.0 \times 10^{11}

Pa,

g = 9.8

m/s

^2

]

(A) $3.60 \times 10^{-8}$
(B) $2.60 \times 10^{-7}$
(C) $1.87 \times 10^{-3}$
(D) $7.07 \times 10^{-4}$

Q220·PhysicsSingle correctJEE Main 2021

A uniform heavy rod of weight 10 kg ms

^{-2}

, cross-sectional area 100 cm

^{2}

and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is

2\times10^{11}

Nm

^{-2}

. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

(A) $2\times10^{-9}$ m
(B) $5\times10^{-8}$ m
(C) $4\times10^{-8}$ m
(D) $5\times10^{-10}$ m

Q221·PhysicsNumericalJEE Main 2021

When a rubber ball is taken to a depth of ______ m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8

\times

10

^{8}

Nm

^{-2}

Density of sea water = 10

^{3}

kgm

^{-3}

g = 9.8 m/s

^{2}

)

Q222·PhysicsSingle correctJEE Main 2021

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius

2.0 \times 10^{-5}

m and density

1.2 \times 10^{3}

kgm

^{-3}

? Take viscosity of liquid =

1.8 \times 10^{-5}

Nsm

^{-2}

. (Neglect buoyancy due to air).

(A) $3.8 \times 10^{-11}$ N
(B) $3.9 \times 10^{-10}$ N
(C) $1.8 \times 10^{-10}$ N
(D) $5.8 \times 10^{-10}$ N

Q223·PhysicsNumericalJEE Main 2021

A rod CD of thermal resistance 10.0

KW^{-1}

is joined at the middle of an identical rod AB as shown in figure, The end A, B and D are maintained at 200

^\circ

C, 100

^\circ

C and 125

^\circ

C respectively. The heat current in CD is P watt. The value of P is ....... .

Q224·PhysicsNumericalJEE Main 2021

Wires

W_1

and

W_2

are made of same material having the breaking stress of 1.25 × 10

^{9}

N/m

^{2}

.

W_1

and

W_2

have cross-sectional area of 8 × 10

^{-7}

m

^{2}

and 4 × 10

^{-7}

m

^{2}

, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _____ kg. (Use g = 10 m/s

^{2}

)

Q225·PhysicsSingle correctJEE Main 2021

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is

\frac{24}{\pi} \times 10^{2}

Nm

^{-2}

. What is the minimum radius of the wire? (Take g = 10 ms

^{-2}

)

(A)125 cm
(B)1250 cm
(C)12.5 cm
(D)1.25 cm

Q226·PhysicsSingle correctJEE Main 2021

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3

\times

10^{-2}

Nm^{-1}

, angle of contact = 0, g = 10

ms^{-2}

and density of water = 1.0

\times

10^{3}

kg

m^{-3}

]

(A)3.62 mm
(B)2.19 mm
(C)5.34 mm
(D)4.97 mm

Q227·PhysicsNumericalJEE Main 2021

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ........ cm.

Q228·PhysicsSingle correctJEE Main 2021

The temperature of equal masses of three different liquids x,y and z are 10°C, 20°C and 30°C respectively. The temperature of mixture when x is mixed with y is 16°C and that when y is mixed with z is 26°C. The temperature of mixture when x and z are mixed will be :

(A)28.32° C
(B)25.62° C
(C)23.84°C
(D)20.28°C

Q229·PhysicsNumericalJEE Main 2021

A stone of mass 20g is projected from a rubber catapult of length 0.1m and area of cross section

10^{-6}

m² stretched by an amount 0.04 m. The velocity of the projected stone is ____ m /s. (Young's modulus of rubber = 0.5×

10^{9}

N/ m² )

Q230·PhysicsNumericalJEE Main 2021

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging stream of water strikes the ground at the maximum range is __________ m.

Q231·PhysicsSingle correctJEE Main 2021

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a << A):

(A)None of these
(B) $\frac{2a}{A}$
(C) $\frac{A}{2a}$
(D) $\frac{a}{A}$

Q232·PhysicsSingle correctJEE Main 2021

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical through its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is : [Density of water f

_w

= 1000 kg m

^{-3}

and Density of air f

_a

= 1.2 kg m

^{-3}

, g = 10 m / s

^2

Coefficient of viscosity of air = 1.8 × 10

^{-5}

Nsm

^{-2}

]

(A)4.94 ms $^{-1}$
(B)14.4 ms $^{-1}$
(C)43.56 ms $^{-1}$
(D)250.6 ms $^{-1}$

Q233·PhysicsSingle correctJEE Main 2021

Two spherical soap bubbles of radii

r_1

and

r_2

in vacuum combine under isothermal conditions. The resulting bubble has radius equal to :

(A) $\sqrt{r_1 r_2}$
(B) $\sqrt{r_1^2 + r_2^2}$
(C) $\frac{r_1 r_2}{r_1 + r_2}$
(D) $\frac{r_1 + r_2}{2}$

Q234·PhysicsSingle correctJEE Main 2021

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are

Y_1

and

Y_2

. The combination behaves as a single wire then its Young's modulus is :

(A) $Y = \frac{Y_1 Y_2}{2\left(Y_1 + Y_2\right)}$
(B) $Y = \frac{2Y_1 Y_2}{3\left(Y_1 + Y_2\right)}$
(C) $Y = \frac{Y_1 Y_2}{Y_1 + Y_2}$
(D) $Y = \frac{2Y_1 Y_2}{Y_1 + Y_2}$

Q235·PhysicsSingle correctJEE Main 2021

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

(A) $\frac{3}{8}$
(B) $\frac{8}{3}$
(C) $\frac{4}{3}$
(D) $\frac{3}{4}$

Q236·PhysicsNumericalJEE Main 2021

The area of cross − section of a railway track is

0.01\,\mathrm{m^2}

. The temperature variation is 10°C, Coefficient of liner expansion of material of track is

10^{-5}

/ °C. The energy stored per meter in the track is ________ J/m. (Young's modulus of material of track is

10^{11}\,\mathrm{Nm^{-2}}

)

Q237·PhysicsSingle correctJEE Main 2021

The value of tension in a long thin metal wire has been changed from

T_1

to

T_2

. The lengths of the metal wire at two different values of tension

T_1

and

T_2

are

\ell_1

and

\ell_2

respectively. The actual length of the metal wire is :

(A) $\frac{T_1\ell_2 - T_2\ell_1}{T_1 - T_2}$
(B) $\sqrt{T_1 T_2 \ell_1 \ell_2}$
(C) $\frac{\ell_1 + \ell_2}{2}$
(D) $\frac{T_1\ell_1 - T_2\ell_2}{T_1 - T_2}$

Q238·PhysicsSingle correctJEE Main 2021

The length of a metal wire is

\ell_1

, when the tension in it is

T_1

and is

\ell_2

when the tension is

T_2

. The natural length of the wire is :

(A) $\sqrt{\ell_1 \ell_2}$
(B) $\dfrac{\ell_1 + \ell_2}{2}$
(C) $\dfrac{\ell_1 T_2 - \ell_2 T_1}{T_2 - T_1}$
(D) $\dfrac{\ell_1 T_2 + \ell_2 T_1}{T_2 + T_1}$

Q239·PhysicsSingle correctJEE Main 2021

Two small drops of mercury each of radius R coalesce to from a single large drop. The ratio of total surface energy before and after the change is :

(A) $2^{\frac{1}{3}} : 1$
(B) $1 : 2^{\frac{1}{3}}$
(C) $2 : 1$
(D) $1 : 2$

Q240·PhysicsNumericalJEE Main 2021

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m

^{2}

. The tank has an opening B near the bottom whose cross-section area is 1 cm

^{2}

. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms

^{-1}

. The value of v, to the nearest integer, is___. [Take value of g to be 10 ms

^{-2}

]

Q241·PhysicsNumericalJEE Main 2021

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is _______ .

Q242·PhysicsSingle correctJEE Main 2021

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

(A) $\frac{ab}{b-a}$
(B) $\frac{a+b}{ab}$
(C) $\frac{b-a}{ab}$
(D) $\frac{ab}{a+b}$

Q243·PhysicsSingle correctJEE Main 2021

Two identical metal wires of thermal conductivities

K_1

and

K_2

respectively are connected in series. The effective thermal conductivity of the combination is :

(A) $\frac{2K_1 K_2}{K_1 + K_2}$
(B) $\frac{K_1 + K_2}{2K_1 K_2}$
(C) $\frac{K_1 + K_2}{K_1 K_2}$
(D) $\frac{K_1 K_2}{K_1 + K_2}$

Q244·PhysicsSingle correctJEE Main 2021

An object is located at 2 km beneath the surface of the water. If the fractional compression

\frac{\Delta V}{V}

is 1.36% , the ratio of hydraulic stress to the corresponding hydraulic strain will be ___________. [Given : density of water is 1000 kg m

^{-3}

and g = 9.8 ms

^{-2}

.]

(A)1.96 × 10 $^{7}$ Nm $^{-2}$
(B)1.44 × 10 $^{7}$ Nm $^{-2}$
(C)2.26 × 10 $^{9}$ Nm $^{-2}$
(D)1.44 × 10 $^{9}$ Nm $^{-2}$

Q245·PhysicsSingle correctJEE Main 2021

The pressure acting on a submarine is 3 × 10

^{5}

Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is 1 × 10

^{5}

Pa density of water is 10

^{3}

kg m

^{-3}

, g = 10 ms

^{-2}

)

(A) $\frac{200}{3}$ %
(B) $\frac{200}{5}$ %
(C) $\frac{5}{200}$ %
(D) $\frac{3}{200}$ %

Q246·PhysicsSingle correctJEE Main 2021

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold both, it will :

(A)Bend towards the right
(B)Not bend but shrink
(C)Neither bend nor shrink
(D)Bend towards the left

Q247·PhysicsSingle correctJEE Main 2021

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min ? The radius of the tap and viscosity of water are 0.5 cm and 10

^{-3}

Pa s, respectively. (Density of water : 10

^{3}

kg/m

^{3}

)

(A)Unsteady to steady flow
(B)Remains steady flow
(C)Remains turbulent flow
(D)Steady flow to unsteady flow

Q248·PhysicsSingle correctJEE Main 2021

The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

(A) $\frac{\rho K}{P}$
(B) $\frac{K}{\rho P}$
(C) $\frac{PK}{\rho}$
(D) $\frac{\rho P}{K}$

Q249·PhysicsSingle correctJEE Main 2021

The length of metallic wire is

l_1

when tension in it is

T_1

. It is

l_2

when the tension is

T_2

. The original length of the wire will be :

(A) $\frac{l_1 + l_2}{2}$
(B) $\frac{T_1 l_1 - T_2 l_2}{T_2 - T_1}$
(C) $\frac{T_2 l_1 + T_1 l_2}{T_1 + T_2}$
(D) $\frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}$

Q250·PhysicsSingle correctJEE Main 2021

The temperature θ at the junction of two insulating sheets, having thermal resistances R

_1

and R

_2

as well as top and bottom temperatures θ

_1

and θ

_2

(as shown in figure) is given by :

(A) $\frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}$
(B) $\frac{\theta_1 R_2 - \theta_2 R_1}{R_2 - R_1}$
(C) $\frac{\theta_2 R_2 - \theta_1 R_1}{R_2 - R_1}$
(D) $\frac{\theta_1 R_1 + \theta_2 R_2}{R_1 + R_2}$

Q251·PhysicsSingle correctJEE Main 2021

A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :

(A) $\frac{2T}{rJ}$
(B) $\frac{3T}{rJ}$
(C) $\frac{2T}{J}\left(\frac{1}{r}-\frac{1}{R}\right)$
(D) $\frac{3T}{J}\left(\frac{1}{r}-\frac{1}{R}\right)$

Q252·PhysicsSingle correctJEE Main 2021

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason R : On heating, the length of the rod increases. In the light of the above statements, choose the corect answer from the options given below :

(A)A is true but R is false
(B)Both A and R are true and R is the correct explanation of A
(C)Both A and R are true but R is NOT the correct explanation of A
(D)A is false but R is true

Q253·PhysicsNumericalJEE Main 2021

A hydraulic press can lift 100 kg when a mass ‘m’ is placed on the smaller piston. It can lift ________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass ‘m’ on the smaller piston.

Q254·PhysicsSingle correctJEE Main 2021

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '

\alpha

'. The metal sheet is heated uniformly, by a small temperature

\Delta

T, so that its new temeprature is T+

\Delta

T. Calculate theincrease in the volume of the metal box-

(A) $\frac{4}{3}\pi a^3\alpha\Delta T$
(B) $4\pi a^3\alpha\Delta T$
(C) $3a^3\alpha\Delta T$
(D) $4a^3\alpha\Delta T$

Q255·PhysicsNumericalJEE Main 2021

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled andsubjected to the same force will be _________ cm.

Q256·PhysicsSingle correctJEE Main 2021

If Y,K and

\eta

are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

(A) $K = \frac{Y\eta}{9\eta - 3Y}$ N/m $^2$
(B) $\eta = \frac{3YK}{9K + Y}$ N/m $^2$
(C) $Y = \frac{9K\eta}{3K - \eta}$ N/m $^2$
(D) $Y = \frac{9K\eta}{2\eta + 3K}$ N/m $^2$

Q257·PhysicsSingle correctJEE Advanced 2020

An open-ended U-tube of uniform cross-sectional area contains water (density

10^{3}

kg

m^{-3}

). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg

m^{-3}

is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio

\left(\frac{h_1}{h_2}\right)

of the heights of the liquid in the two arms is-

(A) $\frac{15}{14}$
(B) $\frac{35}{33}$
(C) $\frac{7}{6}$
(D) $\frac{5}{4}$

Q258·PhysicsNumericalJEE Advanced 2020

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are

10^{3}

kg

m^{-3}

, 0.07

Nm^{-1}

and 10

ms^{-2}

, respectively, the value of h (in mm) is _________.

Q259·PhysicsIntegerJEE Advanced 2020

A train with cross-sectional area

S_t

is moving with speed

v_t

inside a long tunnel of cross-sectional area

S_0

(

S_0 = 4S_t

). Assume that almost all the air (density

\rho

) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be

p_0

. If the pressure in the region between the sides of the train and the tunnel walls is

p

, then

p_0 - p = \frac{7}{2N}\rho v_t^2

. The value of

N

is _________.

Q260·PhysicsMultiple correctJEE Advanced 2020

The filament of a light bulb has surface area 64

mm^2

. The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take Stefan-Boltzmann constant = 5.67 ×

10^{-8}

Wm^{-2}K^{-4}

, Wien's displacement constant = 2.90 ×

10^{-3}

m-K, Planck's constant = 6.63 ×

10^{-34}

Js, speed of light in vacuum= 3.00 ×

10^{8}

ms^{-1}

)-

(A)power radiated by the filament is in the range 642 W to 645 W
(B)radiated power entering into one eye of the observer is in the range 3.15 × $10^{-8}$ W to 3.25 × $10^{-8}$ W
(C)the wavelength corresponding to the maximum intensity of light is 1160 nm
(D)taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range 2.75 × $10^{11}$ to 2.85 × $10^{11}$

Q261·PhysicsNumericalJEE Advanced 2020

A cubical solid aluminium (bulk modulus

= -V\frac{dP}{dV} = 70

GPa) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be

10^3\ \text{kg m}^{-3}

and

10\ \text{ms}^{-2}

, respectively, the change in the edge length of the block in mm is ______.

Q262·PhysicsNumericalJEE Advanced 2020

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is

700\ \text{Wm}^{-2}

and it is absorbed by the water over an effective area of

0.05\ \text{m}^2

. Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in

{}^\circ\text{C}

) in the temperature of water and the surroundings after a long time will be ______________. (Ignore effect of the container, and take constant for Newton's law of cooling

= 0.001\ \text{s}^{-1}

, Heat capacity of water

= 4200\ \text{J kg}^{-1}\ \text{K}^{-1}

)

Q263·PhysicsIntegerJEE Advanced 2020

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is

V

. The balloon is floating at an equilibrium height of 100 m. When

N

number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume

V

remaining unchanged. If the variation of the density of air with height h from the ground is

\rho(h) = \rho_0 e^{-\frac{h}{h_0}}

, where

\rho_0 = 1.25\ \text{kg m}^{-3}

and

h_0 = 6000

m, the value of

N

is __________.

Q264·PhysicsSingle correctJEE Main 2020

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity

K_{1}

,

K_{2}

and

K_{3}

, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between

K_{1}

,

K_{2}

and

K_{2}

is:

(A) $K_{1} : K_{3} = 2 : 3$ , $K_{2} : K_{3} = 2 : 5$
(B) $K_{1} < K_{2} < K_{3}$
(C) $K_{1} : K_{2} = 5 : 2$ , $K_{1} : K_{3} = 3 : 5$
(D) $K_{1} > K_{2} > K_{3}$

Q265·PhysicsSingle correctJEE Main 2020

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms

^{-1}

a ta point where the pressure is P Pascal. At another point where pressure is

\frac{P}{2}

Pascal its speed is V ms

^{-1}

. If the density of the fluid is ρ kg m

^{-3}

and the flow is streamline, then V is equal to:

(A) $\sqrt{\frac{P}{ρ}+v}$
(B) $\sqrt{\frac{2P}{ρ}+v^{2}}$
(C) $\sqrt{\frac{P}{2ρ}+v^{2}}$
(D) $\sqrt{\frac{P}{ρ}+v^{2}}$

Q266·PhysicsSingle correctJEE Main 2020

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is

\frac{27}{8}

w.r.t water, the value of r is.

(A) $\frac{2}{3}$ R
(B) $\frac{4}{9}$ R
(C) $\frac{1}{3}$ R
(D) $\frac{8}{9}$ R

Q267·PhysicsSingle correctJEE Main 2020

Two different wires having lengths

L_1

and

L_2

, and respective temperature coefficient of linear 4expansion

\alpha_1

and

\alpha_2

, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

(A) $\dfrac{\alpha_1+\alpha_2}{2}$
(B) $2\sqrt{\alpha_1\alpha_2}$
(C) $\dfrac{\alpha_1 L_1 + a_2 L_2}{L_1+L_2}$
(D) $4\dfrac{\alpha_1\alpha_2}{\alpha_1+\alpha_2}\dfrac{L_1 L_2}{(L_2+L_1)^{2}}$

Q268·PhysicsSingle correctJEE Main 2020

A bullet of mass 5 g, traveling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is

0.030\,\text{cal}/(\text{g-}^{0}\text{C})

(1\text{cal}=4.2\times10^{7}\text{ ergs})

close to:

(A) $83.3^{0}$ C
(B) $38.4^{0}$ C
(C) $87.5^{0}$ C
(D) $119.2^{0}$ C

Q269·PhysicsSingle correctJEE Main 2020

In an experiment to verify Stokes law, a small spherical ball of radius r and density

\rho

falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to: (ignore viscosity of air)

(A) $r^{3}$
(B) $r^{4}$
(C) $r^{2}$
(D) $r$

Q270·PhysicsSingle correctJEE Main 2020

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s

^{-2}

. The density of water is 1 gm cm

^{-3}

and water offers negligible drag force on the bubble. The mass of the bubble is: (g = 980 cm/s

^{2}

).

(A)4.51 gm
(B)1.52 gm
(C)3.15 gm
(D)4.15 gm

Q271·PhysicsSingle correctJEE Main 2020

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B =

8 \times 10^{10}

Pa)

(A)0.6
(B)5
(C)1.67
(D)20

Q272·PhysicsSingle correctJEE Main 2020

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is :

(A) $\frac{3}{4}gdS\left(x_2 - x_1\right)^{2}$
(B) $gdS\left(x_2 + x_1\right)^{2}$
(C) $\frac{1}{4}gdS\left(x_2 - x_1\right)^{2}$
(D) $gdS\left(x_2^{2} + x_1^{2}\right)$

Q273·PhysicsSingle correctJEE Main 2020

The specific heat of water = 4200 J kg

^{-1}

K

^{-1}

and the latent heat of ice =

3.4 \times 10^{5}

J kg

^{-1}

. 100 grams of ice at 0°C is placed in 200 g of water at 25°C. The amount of ice that will melt as the temperature of water reaches 0°C is close to (in grams):

(A)64.6
(B)61.7
(C)69.3
(D)63.8

Q274·PhysicsSingle correctJEE Main 2020

A calorimeter of water equivalent 20 g contains 180 g of water at

25^{\circ}C

, 'm' grams of steam at

100^{\circ}C

is mixed in it till the temperature of the mixture is

31^{\circ}C

. The value of 'm' is close to (Latent heat of water = 540 cal g

^{-1}

, specific heat of water

= 1\,\mathrm{cal}\,g^{-1}\,^{\circ}C^{-1}

)

(A)2.6
(B)4
(C)2
(D)3.2

Q275·PhysicsSingle correctJEE Main 2020

A metallic sphere cools from

50^{\circ}C

to

40^{\circ}

in 300s. If atmospheric temperature around is

20^{\circ}C

, then the sphere's temperature after the next 5 minutes will be close to:

(A) $35^{\circ}C$
(B) $31^{\circ}C$
(C) $33^{\circ}C$
(D) $28^{\circ}C$

Q276·PhysicsNumericalJEE Main 2020

When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0°, the surface tension of the liquid, in milli Newton

m^{-1}

, is [

\rho_{(lliquid)}

= 900

kgm^{-3}

, g = 10

ms^{-2}

] (Give answer in closest integer)

Q277·PhysicsSingle correctJEE Main 2020

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is

(A)4 : 1
(B)0.8 : 1
(C)2 : 1
(D)8 : 1

Q278·PhysicsNumericalJEE Main 2020

A bakelite beaker has volume capacity of 500 cc at 30°C. When it is partially filled with

V_m

volume (at 30°C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If

\gamma_{(beaker)}

= 6 ×

10^{-6}

°

C^{-1}

and

\gamma_{(mercury)}

= 1.5 ×

10^{-4}

°

C^{-1}

, where γ is the coefficient of volume expansion, then

V_m

(in cc) is close to __________.

Q279·PhysicsSingle correctJEE Main 2020

A small spherical droplet of density d is floating exactly half immersed in a liquid of density ρ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet):

(A) $r = \sqrt{\frac{3T}{(2d - \rho)g}}$
(B) $r = \sqrt{\frac{T}{(d - \rho)g}}$
(C) $r = \sqrt{\frac{2T}{3(d + \rho)g}}$
(D) $r = \sqrt{\frac{T}{(d + \rho)g}}$

Q280·PhysicsNumericalJEE Main 2020

A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s

^{-1}

) with which it can be rotated about its other end in space station is (Breaking stress of wire =

4.8 \times 10^{7}

Nm

^{-2}

and area of cross-section of the wire =

10^{-2}

cm

^{2}

) is

Q281·PhysicsSingle correctJEE Main 2020

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is

(A) $1 : \sqrt{2}$
(B) $2 : 1$
(C) $\sqrt{2} : 1$
(D) $1 : 2$

Q282·PhysicsSingle correctJEE Main 2020

Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm

^{-2}

between A and B where the area of cross section are 40 cm

^{2}

and 20 cm

^{2}

, respectively. Find the rate of flow of water through the tube. (density of water = 1000 kg m

^{-3}

)

(A)1810 cm $^{3}$ /s
(B)2420 cm $^{3}$ /s
(C)2720 cm $^{3}$ /s
(D)3020 cm $^{3}$ /s

Q283·PhysicsSingle correctJEE Main 2020

A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion is floating vertically in water at

0^{\circ}

C such that its height above the water surface is 20 cm. When the temperature of water is increased to

4^{\circ}

C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T =

4^{\circ}

C, relative to the density at T =

0^{\circ}

C is close to:

(A)1.01
(B)1.26
(C)1.04
(D)1.03

Q284·PhysicsSingle correctJEE Main 2020

Two liquids of densities

\rho_{1}

and

\rho_{2}

(

\rho_{2}

= 2

\rho_{1}

) are filled up behind a square wall of inside 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):

(A)1/2
(B)1/4
(C)2/3
(D)1/3

Q285·PhysicsSingle correctJEE Main 2020

Consider a solid sphere of radius R and mass density

p(r) = p_{0}\left(1 - \dfrac{r^{2}}{R^{2}}\right)

,

0 < r \leq R

. The minimum density of a liquid in which it will float is

(A) $\dfrac{p_{0}}{5}$
(B) $\dfrac{2p_{0}}{5}$
(C) $\dfrac{2p_{0}}{3}$
(D) $\dfrac{p_{0}}{3}$

Q286·PhysicsNumericalJEE Main 2020

Three containers C

_1

, C

_2

and C

_3

have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process) The value of

\theta

(in °C to the nearest integer) is ____.

C $_1$	C $_2$	C $_3$	T
1 l	2 l	—	60°C
—	1 l	2 l	30°C
2 l	—	1 l	60°C
1 l	1 l	1 l	$\theta$

Q287·PhysicsSingle correctJEE Main 2020

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0

mm^{2}

) is 90

ms^{-1}

. If the young's modulus of wire is

16 \times 10^{11}

Nm^{-2}

, the extension of wire over its natural length is:

(A)0.03 mm
(B)0.01 mm
(C)0.02 mm
(D)0.04 mm

Q288·PhysicsNumericalJEE Main 2020

M grams of steam at 100°C is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40°C [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g], the value of M is __________.

Q289·PhysicsNumericalJEE Main 2020

A non-isotropic solid metal cube has coefficients of linear expansion as:

5 \times 10^{-5}

/°C along the x = axis and

5 \times 10^{-6}

/°C along the y and the z-axis. If coefficient of volume expansion of the solid C

\times 10^{-6}

/°C then the value of C is _________.

Q290·PhysicsSingle correctJEE Main 2020

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

(A) $\frac{3}{4}$
(B) $\frac{81}{256}$
(C) $\frac{\sqrt{3}}{2}$
(D) $\frac{9}{16}$

Q291·PhysicsNumericalJEE Advanced 2019

A liquid at 30°C is poured very slowly into a Calorimeter that is at temperature of 110°C. The boiling temperature of the liquid is 80°C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50°C. The ratio of the Latent heat of the liquid to its specific heat will be ______ °C. [Neglect the heat exchange with surrounding]

Q292·PhysicsMultiple correctJEE Advanced 2019

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries

T_1

and

T_2

of different materials having water contact angles of

0^0

and

60^0

, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is (are) correct? [Surface tension of a water = 0.075 N/m, density of water = 1000 kg/

m^3

, take g = 10 m/

s^2

]

(A)For case I, if the joint is kept at 8 cm above the water surface, the height of water column in the tube will be 7.5 cm. (Neglect the weight of the water in the meniscus)
(B)For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm. (Neglect the weight of the water in the meniscus)
(C)For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of the water in the meniscus)
(D)The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.

Q293·PhysicsNumericalJEE Advanced 2019

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area 0.5

cm^2

and, length

\sqrt{3}

m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30° and 60°, respectively. If elongation in copper wire is

\left(\Delta\ell_C\right)

and elongation in steel wire is

\left(\Delta\ell_S\right)

, then the ratio

\frac{\Delta\ell_C}{\Delta\ell_S}

is ______ [Young's modulus for copper and steel are 1 ×

10^{11}

N/

m^2

and 2 ×

10^{11}

N/

m^2

, respectively.]

Q294·PhysicsSingle correctJEE Main 2019

A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to :

(A) $9F/(\pi r^{2}YT)$
(B) $F/(3\pi r^{2}YT)$
(C) $3F/(\pi r^{2}YT)$
(D) $6F/(\pi r^{2}YT)$

Q295·PhysicsSingle correctJEE Main 2019

When

M_1

gram of ice at

-10

ºC (specific heat = 0.5 cal g

^{-1}

°C

^{-1}

) is added to

M_2

gram of water at 50ºC, finally no ice is left and the water is at 0ºC. The value of latent heat of ice, in cal g

^{-1}

is:

(A) $\dfrac{50M_2}{M_1}-5$
(B) $\dfrac{5M_2}{M_1}-5$
(C) $\dfrac{50M_2}{M_1}$
(D) $\dfrac{5M_1}{M_2}-50$

Q296·PhysicsSingle correctJEE Main 2019

A solid sphere, of radius R acquires a terminal velocity v

_{1}

when falling (due to gravity) through a viscous fluid having a coefficient of viscosity

\eta

. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v

_{2}

, when falling through the same fluid, the ratio (v

_{1}

/v

_{2}

) equals :

(A)27
(B)1/27
(C)9
(D)1/9

Q297·PhysicsSingle correctJEE Main 2019

One kg of water, at 20ºC, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 Ω. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = 4200 J/kg ºC), Latent heat of water = 2260 kJ/kg]

(A)3 minutes
(B)10 minutes
(C)22 minutes
(D)16 minutes

Q298·PhysicsSingle correctJEE Main 2019

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

(A)1.00 mm
(B)1.16 mm
(C)0.90 mm
(D)1.36 mm

Q299·PhysicsSingle correctJEE Main 2019

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r

_{1}

, while water rises by the same amount h in a capillary tube of radius r

_{2}

. The ratio, (r

_{1}

/r

_{2}

), is then close to:

(A)3/5
(B)4/5
(C)2/3
(D)2/5

Q300·PhysicsSingle correctJEE Main 2019

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take density of water =

10^{3}

kg/m

^{3}

]

(A)46.3 kg
(B)65.4 kg
(C)30.1 kg
(D)87.5 kg

Q301·PhysicsSingle correctJEE Main 2019

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms

^{-1}

. The cross-sectional area of the tap is

10^{-4}

m

^{2}

. Assume that the pressure is constant throughout the stream of water and that flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be: (take g = 110 ms

^{-2}

)

(A) $5 \times 10^{-4}$ m $^{2}$
(B) $5 \times 10^{-5}$ m $^{2}$
(C) $1 \times 10^{-5}$ m $^{2}$
(D) $2 \times 10^{-5}$ m $^{2}$

Q302·PhysicsSingle correctJEE Main 2019

A submarine experiences a pressure of

5.05 \times 10^{6}

Pa at a depth of d

_1

in a sea. When it goes further to a depth of d

_2

, it experiences a pressure of

8.08 \times 10^{6}

Pa. Then d

_2

− d

_1

is approximately (density of water =

10^{3}

kg/m

^{3}

and acceleration due to gravity = 10 ms

^{-2}

)

(A)400 m
(B)500 m
(C)600 m
(D)300 m

Q303·PhysicsSingle correctJEE Main 2019

If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is:

(A)4 M
(B) $\frac{M}{2}$
(C)M
(D)2 M

Q304·PhysicsSingle correctJEE Main 2019

Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are

\theta_{2}

and

\theta_{1}

respectively

(\theta_{2} > \theta_{1})

. The temperature at the interface is:

(A) $\dfrac{\theta_{2} + \theta_{1}}{2}$
(B) $\dfrac{\theta_{1}}{10} + \dfrac{9\theta_{2}}{10}$
(C) $\dfrac{\theta_{1}}{3} + \dfrac{2\theta_{2}}{3}$
(D) $\dfrac{\theta_{1}}{6} + \dfrac{5\theta_{2}}{6}$

Q305·PhysicsSingle correctJEE Main 2019

A wooden block floating in a bucket of water has

\dfrac{4}{5}

of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:-

(A)0.5
(B)0.7
(C)0.6
(D)0.8

Q306·PhysicsSingle correctJEE Main 2019

A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)

(A) $10^{-3}$ K
(B) $10^{-4}$
(C) $10^{-1}$ K
(D) $10^{-5}$ K

Q307·PhysicsSingle correctJEE Main 2019

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of

8 \times 10^{2}

kg/m

^{3}

and specific heat of 2000 J kg

^{-1}

K

^{-1}

while liquid in B has density of

10^{3}

kg m

^{-3}

and specific heat of 4000 J Kg

^{-1}

K

^{-1}

. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q308·PhysicsSingle correctJEE Main 2019

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that

g = 3.1\pi

m s

^{-2}

, what will be the tensile stress that would be developed in the wire?

(A) $6.2 \times 10^{6}$ N m $^{-2}$
(B) $4.8 \times 10^{6}$ N m $^{-2}$
(C) $5.2 \times 10^{6}$ N m $^{-2}$
(D) $3.1 \times 10^{6}$ N m $^{-2}$

Q309·PhysicsSingle correctJEE Main 2019

Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m

^{3}

, coefficient of viscosity of water = 1 mPa s)

(A) $10^{3}$
(B) $10^{6}$
(C) $10^{2}$
(D) $10^{4}$

Q310·PhysicsSingle correctJEE Main 2019

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 m s

^{-1}

. Neglect the change in the area of cross section of the cord while stretched. The Young's modulus of rubber is closest to:

(A) $10^{3}$ N m $^{-2}$
(B) $10^{6}$ N m $^{-2}$
(C) $10^{8}$ N m $^{-2}$
(D) $10^{4}$ N m $^{-2}$

Q311·PhysicsSingle correctJEE Main 2019

A thermally insulted vessel contains 150 g of water at

0°C

. Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at

0°C

itself. The mass of evaporated water will be closes to: (Latent heat of vaporization of water

=2.10\times10^{6}Jkg^{-1}

and Laten heat of Fusion of water

=3.36\times10^{5}Jkg^{-1}

)

(A)35 g
(B)150 g
(C)130 g
(D)20 g

Q312·PhysicsSingle correctJEE Main 2019

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to:

(A)1.3 mm
(B)1.5 mm
(C)1.7 mm
(D)1.9 mm

Q313·PhysicsSingle correctJEE Main 2019

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :

(A)2.0
(B)0.1
(C)0.4
(D)1.2

Q314·PhysicsSingle correctJEE Main 2019

A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:

(A)3.0 mm
(B)4.0 mm
(C)5.0 mm
(D)zero

Q315·PhysicsSingle correctJEE Main 2019

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is

K_1

and that of the outer cylinder is

K_2

. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:

(A) $\dfrac{K_1+K_2}{2}$
(B) $K_1+K_2$
(C) $\dfrac{2K_1+3K_2}{5}$
(D) $\dfrac{K_1+3K_2}{4}$

Q316·PhysicsSingle correctJEE Main 2019

A thermometer graduated according to a linear scale reads a value x

_0

when in contact with boiling water, and x

_0

/3 when in contact with ice. What is the temperature of an object in °C, if this thermometer in the contact with the object reads x

_0

/2?

(A)25
(B)60
(C)40
(D)45

Q317·PhysicsSingle correctJEE Main 2019

A metal bal of mass 0.1 kg is heated upto 500

^{\circ}

C and dropped into a vessel of heat capacity 800 JK

^{-1}

and containing 0.5 kg water. The initial temperature of water and vessel is 30

^{\circ}

C. What is the approximate percentage increment in the temperature of the water? [Specific heat Capacities of water and metal are, respectively 4200 Jkg

^{-1}

K

^{-1}

and 400 jkg

^{-1}

K

^{-1}

]

(A)15%
(B)30%
(C)25%
(D)20%

Q318·PhysicsSingle correctJEE Main 2019

Ice at –20

^{0}

C is added to 50 g of water at 40

^{0}

C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/

^{0}

C) Heat of fusion of water at 0°C = 334 J/g)

(A)50 g
(B)100 g
(C)60 g
(D)40 g

Q319·PhysicsSingle correctJEE Main 2019

When 100g of a liquid A at 100°C is added to 50g of a liquid B at temperature 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100g of liquid A at 100°C is added to 50g of liquid B at 50°C, will be:

(A)85°C
(B)60°C
(C)80°C
(D)70°C

Q320·PhysicsSingle correctJEE Main 2019

Two rods A and B of identical dimensions are at temperature

30^{\circ}\text{C}

. If a heated upto

180^{\circ}\text{C}

and B upto

\text{T}^{\circ}\text{C}

, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4:3, then the value of T is:

(A) $230^{\circ}\text{C}$
(B) $270^{\circ}\text{C}$
(C) $200^{\circ}\text{C}$
(D) $250^{\circ}\text{C}$

Q321·PhysicsSingle correctJEE Main 2019

A liquid of density

\rho

is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be:

(A) $\dfrac{1}{4}\rho v^{2}$
(B) $\dfrac{3}{4}\rho v^{2}$
(C) $\dfrac{1}{2}\rho v^{2}$
(D) $\rho v^{2}$

Q322·PhysicsSingle correctJEE Main 2019

A heat source at T

= 10^{3}

K is connected to another heat reservoir at T

= 10^{2}

K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 WK

^{-1}

m

^{-1}

, the energy flux through it in the steady state is:

(A)90 Wm $^{-2}$
(B)120 Wm $^{-2}$
(C)65 Wm $^{-2}$
(D)200 Wm $^{-2}$

Q323·PhysicsSingle correctJEE Main 2019

Water flows into a large tank with flat bottom at the rate of

10^{-4}

m

^{3}

s

^{-1}

. Water is also leaking out of a hole of area 1 cm

^{2}

at its bottom. If the height of the water in the tank remains steady, then this height is:

(A)5.1 cm
(B)1.7 cm
(C)4 cm
(D)2.9 cm

Q324·PhysicsSingle correctJEE Main 2019

The top of a water tank is open to air and its water level is maintained. It is giving out

0.74\ m^{3}

water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

(A)6.0 m
(B)4.8 m
(C)9.6 m
(D)2.9 m

Q325·PhysicsSingle correctJEE Main 2019

Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length

\dfrac{3L}{2}

, is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to:

(A)45°C
(B)75°C
(C)60°C
(D)35°C

Q326·PhysicsSingle correctJEE Main 2019

A rod of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion

\alpha

/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by

\Delta T

K. Young's modulus, Y, for this metal is

(A) $\frac{F}{A\alpha \Delta T}$
(B) $\frac{F}{A\alpha(\Delta T-273)}$
(C) $\frac{F}{2A \alpha \Delta T}$
(D) $\frac{2F}{A \alpha \Delta T}$

Q327·PhysicsMultiple correctJEE Advanced 2018

Consider a thin square plate floating on a viscous liquid in a large tank. The height

h

of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity

u_{0}

. Which of the following statements is (are) true?

(A)The resistive force of liquid on the plate is inversely proportional to $h$
(B)The resistive force of liquid on the plate is independent of the area of the plate
(C)The tangential (shear) stress on the floor of the tank increases with $u_{0}$
(D)The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

Q328·PhysicsNumericalJEE Advanced 2018

A steel wire of diameter 0.5 mm and Young's modulus

2 \times 10^{11}

Nm

^{-2}

carries a load of mass M. The length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is ___________. Take g = 10 ms

^{-2}

and is

\pi

= 3.2.

Q329·PhysicsNumericalJEE Advanced 2018

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures

T_{1} = 300\ K

and

T_{2} = 100\ K

, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are

K_{1}

and

K_{2}

respectively. If the temperature at the junction of the two cylinders in the steady state is

200\ K

, then

K_{1}/K_{2} =

__________.

Q330·PhysicsMultiple correctJEE Advanced 2018

A uniform capillary tube of inner radius

r

is dipped vertically into a beaker filled with water. The water rises to a height

h

in the capillary tube above the water surface in the beaker. The surface tension of water is

\sigma

. The angle of contact between water and the wall of the capillary tube is

\theta

. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

(A)For a given material of the capillary tube, h decreases with increase in $r$
(B)For a given material of the capillary tube, h is independent of $\sigma$
(C)If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases
(D) $h$ is proportional to contact angle $\theta$

Q331·PhysicsIntegerJEE Advanced 2017

A drop of liquid of radius R =

10^{-2}

m having surface tension S =

\frac{0.1}{4\pi}

Nm^{-1}

divides itself into K identical drops. In this process the total change in the surface energy

\Delta U = 10^{-3}

J. If K =

10^{\alpha}

then the value of

\alpha

is

Q332·PhysicsIntegerJEE Advanced 2016

Consider two solid spheres P and Q each of density

8\ \text{gm cm}^{-3}

and diameters 1cm and 0.5cm, respectively. Sphere P is dropped into a liquid of density

0.8\ \text{gm cm}^{-3}

and viscosity

\eta = 3

poiseulles. Sphere Q is dropped into a liquid of density

1.6\ \text{gm cm}^{-3}

and viscosity

\eta = 2

poiseulles. The ratio of the terminal velocities of P and Q is

Q333·PhysicsSingle correctJEE Advanced 2016

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10

^{0}

C. Now the end P is maintained at 10

^{0}

C, while the end S is heated and maintained at 400

^{0}

C. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is

1.2 \times 10^{-5}\ \text{K}^{-1}

, the change in length of the wire PQ is

(A)0.78 mm
(B)0.90 mm
(C)1.56 mm
(D)2.34 mm

Q334·PhysicsMultiple correctJEE Advanced 2015

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at

r

(r < R)

, then the correct option(s) is(are)

(A) $P(r = 0) = 0$
(B) $\dfrac{P(r = 3R/4)}{P(r = 2R/3)} = \dfrac{63}{80}$
(C) $\dfrac{P(r = 3R/5)}{P(r = 2R/5)} = \dfrac{16}{21}$
(D) $\dfrac{P(r = R/2)}{P(r = R/3)} = \dfrac{20}{27}$

Q335·PhysicsMultiple correctJEE Advanced 2015

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)

(A)P has more tensile strength than Q
(B)P is more ductile than Q
(C)P is more brittle than Q
(D)The Young's modulus of P is more than that of Q

Q336·PhysicsMultiple correctJEE Advanced 2015

Two spheres P and Q of equal radii have densities

\rho_{1}

and

\rho_{2}

, respectively. The spheres are connected by a massless string and placed in liquids

L_{1}

and

L_{2}

of densities

\sigma_{1}

and

\sigma_{2}

and viscosities

\eta_{1}

and

\eta_{2}

, respectively. They float in equilibrium with the sphere P in

L_{1}

and sphere Q in

L_{2}

and the string being taut (see figure). If sphere P alone in

L_{2}

has terminal velocity

\vec{V}_{P}

and Q alone in

L_{1}

has terminal velocity

\vec{V}_{Q}

, then

(A) $\dfrac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|} = \dfrac{\eta_{1}}{\eta_{2}}$
(B) $\dfrac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|} = \dfrac{\eta_{2}}{\eta_{1}}$
(C) $\vec{V}_{P} \cdot \vec{V}_{Q} > 0$
(D) $\vec{V}_{P} \cdot \vec{V}_{Q} < 0$

Q337·PhysicsSingle correctJEE Advanced 2014

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere. If the density of air is

\rho_{a}

and that of the liquid

\rho_{\ell}

, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

(A) $\sqrt{\frac{\rho_{a}}{\rho_{\ell}}}$
(B) $\sqrt{\rho_{a}\rho_{\ell}}$
(C) $\sqrt{\frac{\rho_{\ell}}{\rho_{a}}}$
(D) $\rho_{\ell}$

Q338·PhysicsSingle correctJEE Advanced 2014

Parallel rays of light of intensity

I = 912

Wm

^{-2}

are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant

\sigma = 5.7 \times 10^{-8}

Wm

^{-2}

K

^{-4}

and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

(A)330 K
(B)660 K
(C)990 K
(D)1550 K

Q339·PhysicsSingle correctJEE Advanced 2014

A glass capillary tube is of the shape of truncated cone with an apex angle

\alpha

so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height

h

, where the radius of its cross section is

b

. If the surface tension of water is

S

, its density is

\rho

, and its contact angle with glass is

\theta

, the value of

h

will be (

g

is the acceleration due to gravity)

(A) $\frac{2S}{b\rho g}\cos(\theta - \alpha)$
(B) $\frac{2S}{b\rho g}\cos(\theta + \alpha)$
(C) $\frac{2S}{b\rho g}\cos(\theta - \alpha/2)$
(D) $\frac{2S}{b\rho g}\cos(\theta + \alpha/2)$

Q340·PhysicsIntegerJEE Advanced 2014

During Searle's experiment, zero of the Vernier scale lies between

3.20 \times 10^{-2} \text{ m}

and

3.25 \times 10^{-2} \text{ m}

of the main scale. The

20^{\text{th}}

division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of

2 \text{ kg}

is applied to the wire, the zero of the Vernier scale still lies between

3.20 \times 10^{-2} \text{ m}

and

3.25 \times 10^{-2} \text{ m}

of the main scale but now the

45^{\text{th}}

division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is

2 \text{ m}

and its cross-sectional area is

8 \times 10^{-7} \text{ m}^2

. The least count of the Vernier scale is

1.0 \times 10^{-5} \text{ m}

. The maximum percentage error in the Young's modulus of the wire is

Q341·PhysicsSingle correctJEE Advanced 2014

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance

d

of 1.2 m from the person. In the following, state of the lift's motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the lists.

List I	List II
P.Lift is accelerating vertically up.	1. $d = 1.2$ m
Q.Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.	2. $d > 1.2$ m
R.Lift is moving vertically up with constant speed.	3. $d < 1.2$ m
S.Lift is falling freely.	4.No water leaks out of the jar

(A)P-2, Q-3, R-2, S-4
(B)P-2, Q-3, R-1, S-4
(C)P-1, Q-1, R-1, S-4
(D)P-2, Q-3, R-1, S-1

Q342·PhysicsSingle correctJEE Advanced 2014

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere. If the piston is pushed at a speed of 5 mms

^{-1}

, the air comes out of the nozzle with a speed of

(A)0.1 ms $^{-1}$
(B)1 ms $^{-1}$
(C)2 ms $^{-1}$
(D)8 ms $^{-1}$

Q343·PhysicsMultiple correctJEE Advanced 2013

A solid sphere of radius R and density

\rho

is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density

3\rho

. The complete arrangement is placed in a liquid of density

2\rho

and is allowed to reach equilibrium. The correct statement(s) is (are)

(A)the net elongation of the spring is $\frac{4\pi R^{3}\rho g}{3k}$
(B)the net elongation of the spring is $\frac{8\pi R^{3}\rho g}{3k}$
(C)the light sphere is partially submerged.
(D)the light sphere is completely submerged.

Q344·PhysicsSingle correctJEE Advanced 2013

One end of a horizontal thick copper wire of length

2L

and radius

2R

is welded to an end of another horizontal thin copper wire of length

L

and radius

R

. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

(A)0.25
(B)0.50
(C)2.00
(D)4.00

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