How many questions from Work, Energy and Power appear in JEE?

Work, Energy and Power has appeared in 132 of the last 186 JEE Main and JEE Advanced papers — about 71% of them — contributing 169 questions in total across those papers.

Is Work, Energy and Power an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 71% 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 Work, Energy and Power 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.

Work, Energy and Power JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Main 2026

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is ________ J. (take g = 10 m/s²)

(A)−8.75
(B)−8.35
(C)−9.55
(D)−9.98

Q2·PhysicsSingle correctJEE Main 2026

A body of mass 1 kg moves along a straight line with a velocity

v = 2x^{2}

. The work done by the body during displacement from

x = 0

to 5 m is __________ J.

(A)0
(B)250
(C)1250
(D)1000

Q3·PhysicsSingle correctJEE Main 2026

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height h as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h = αR. The value of α is ________.

(A)2
(B)4
(C)3
(D)6

Q4·PhysicsSingle correctJEE Main 2026

A mass of 1 kg is kept on an inclined plane with 30° inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is ________ J. (Take g = 10 m/s²)

(A)20
(B)25
(C)30
(D)10

Q5·PhysicsNumericalJEE Main 2026

A 1 kg block subjected to two simultaneous forces

(2\hat{i} + 3\hat{j} + 4\hat{k})

N and

(3\hat{i} - \hat{j} - 2\hat{k})

N is moved a distance of 25 m along

(3\hat{i} - 4\hat{j})

direction. The work done in this process is ______ J.

Q6·PhysicsNumericalJEE Main 2026

A body of mass 2 kg begins to move under the influence of time dependent force

\vec{F} = (2t\hat{i} + 6t^2\hat{j})

N, where

\hat{i}

and

\hat{j}

are unit vectors along

x

and

y

-axis respectively. The power produced by the force at

t = 2

s is ______ W.

Q7·PhysicsSingle correctJEE Main 2026

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is ______ N. (Take

g = 10

m/s

^{2}

)

(A)1980
(B)2020
(C)2000
(D)1000

Q8·PhysicsSingle correctJEE Main 2026

In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle

30^\circ

shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)

(A) $\sqrt{5gr}$
(B) $\sqrt{\frac{7}{2}gr}$
(C) $\sqrt{4gr}$
(D) $\sqrt{\frac{5}{2}gr}$

Q9·PhysicsSingle correctJEE Main 2026

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in °C), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31 cal/kg. °C and 1 cal = 4.2 J)

(A) $1.75$
(B) $1.44$
(C) $1.15$
(D) $1.95$

Q10·PhysicsSingle correctJEE Main 2026

A small both A of mass m is attached to a massless rigid rod of length 1m pivoted at point P and kept at an angle of 60° with vertical as shown in figure. At distance of 1m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is _______m.

(A) $\frac{3}{5}$
(B) $\frac{1}{5}$
(C) $\frac{2+\sqrt{3}}{5}$
(D) $\frac{2-\sqrt{3}}{5}$

Q11·PhysicsSingle correctJEE Main 2026

Two blocks with masses 100g and 200g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants

k_A

,

k_B

of A and B, respectively satisfy the relation

4k_A = 3k_B

, is :

(A)4E
(B)2E
(C)3E
(D) $\frac{4}{3}E$

Q12·PhysicsSingle correctJEE Main 2026

A bead

P

sliding on a frictionless semi-circular string

(ACB)

and it is at point

S

at t = 0 and at this instant the horizontal component of its velocity is

v

. Another bead

Q

of the same mass as

P

is ejected from point

A

at t = 0 along the horizontal string

AB

, with the speed

v

, friction between the beads and the respective strings may be neglected in both cases. Let

t_{p}

and

t_{Q}

be the respective times taken by beads

P

and

Q

to reach the point

B

, then the relation between

t_{p}

and

t_{Q}

is

(A) $t_{P} > t_{Q}$
(B) $t_{p} < t_{Q}$
(C) $t_{p} > 1.25 t_{Q}$
(D) $t_{p} = t_{Q}$

Q13·PhysicsSingle correctJEE Main 2026

Given below are two statements : Statement I : An object moves from position

r_1

to position

r_2

under a conservative force field

\vec{F}

. The work done by the force is

W = -\int_{r_1}^{r_2} \vec{F} \cdot \vec{dr}

. Statement II : Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :

(A)Both Statement I and Statement II are true
(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 false

Q14·PhysicsSingle correctJEE Main 2026

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by

\text{x(t)} = \alpha\text{t}^2 + \beta\text{t} + \gamma\,\text{m}

, where

\alpha = 1\ \text{m/s}^2

,

\beta = 1

m/s and

\gamma = 1

m. The work done on the body during the time interval t = 2 s to t = 3 s, is ________ J.

(A)49
(B)42
(C)24
(D)12

Q15·PhysicsSingle correctJEE Main 2026

Potential energy (

V

) versus distance (

x

) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

(A) $F_{BC} > F_{CD} > F_{DE} > F_{AB}$
(B) $F_{CD} > F_{AB} > F_{BC} > F_{DE}$
(C) $F_{CD} > F_{DE} > F_{AB} > F_{BC}$
(D) $F_{BC} > F_{AB} > F_{DE} > F_{CD}$

Q16·PhysicsSingle correctJEE Advanced 2025

In a scattering experiment, a particle of mass 2m collides with another particle of mass m, which is initially at rest. Assuming the collision to be perfectly elastic, the maximum angular deviation

\theta

of the heavier particle, as shown in the figure, in radians is:

(A) $\pi$
(B) $\tan^{-1}\left(\frac{1}{2}\right)$
(C) $\frac{\pi}{3}$
(D) $\frac{\pi}{6}$

Q17·PhysicsSingle correctJEE Main 2025

An object of mass 1000 g experiences a time dependent force

\vec{F}=(2t\hat{i}+3t^2\hat{j})

N. The power generated by the force at time

t

is:

(A) $(2t^2+3t^3)$ W
(B) $(2t^2+18t^3)$ W
(C) $(3t^3+5t^5)$ W
(D) $(2t^3+3t^5)$ W

Q18·PhysicsSingle correctJEE Main 2025

Which one of the following forces cannot be expressed in terms of potential energy?

(A)Coulomb's force
(B)Gravitational force
(C)Frictional force
(D)Restoring force

Q19·PhysicsSingle correctJEE Main 2025

Two cylindrical vessels of equal cross sectional area of

2\,\mathrm{m}^2

contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is: (Density of water is

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

and

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

)

(A) $1\times10^5$ J
(B) $4\times10^5$ J
(C) $6\times10^5$ J
(D) $8\times10^5$ J

Q20·PhysicsSingle correctJEE Main 2025

A particle is released from height

S

above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively:

(A) $\dfrac{S}{2},\ \sqrt{\dfrac{3gS}{2}}$
(B) $\dfrac{S}{2},\ \dfrac{3gS}{2}$
(C) $\dfrac{S}{4},\ \dfrac{3gS}{2}$
(D) $\dfrac{S}{4},\ \sqrt{\dfrac{3gS}{2}}$

Q21·PhysicsSingle correctJEE Main 2025

A block of mass 1 kg, moving along the x-axis with speed

v=10

m/s enters a rough region ranging from

x=0.1

m to

x=1.9

m. The retarding force acting on the block in this range is

F_r=-kx

N, with

k=10

N/m. Then the final speed of the block as it crosses the rough region is:

(A)10 m/s
(B)4 m/s
(C)6 m/s
(D)8 m/s

Q22·PhysicsSingle correctJEE Main 2025

Consider two blocks A and B of masses

m_1=10

kg and

m_2=5

kg are placed on a frictionless table. The block A moves with a constant speed

v=3

m/s towards the block B kept at rest. A spring with spring constant

k=3000

N/m is attached with the block B. After the collision, suppose that the blocks A and B, along with the spring in contact compression state, move together, then the compression in the spring is (neglect the mass of the spring):

(A)0.2 m
(B)0.4 m
(C)0.1 m
(D)0.3 m

Q23·PhysicsSingle correctJEE Main 2025

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities

v_A=5

m/s,

v_B=2

m/s,

v_C=4

m/s (arranged A, B, C from left to right and all moving in the +x direction). If we wait sufficiently long for elastic collisions to happen, then

v_A=4

m/s,

v_B=2

m/s,

v_C=5

m/s will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. 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)(A) is true but (R) is false
(C)Both (A) and (R) are true and (R) is the correct explanation of (A).
(D)(A) is false but (R) is true

Q24·PhysicsSingle correctJEE Main 2025

As shown below, bob A of a pendulum having massless string of length ‘R’ is released from

60^\circ

to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity)

(A) $\dfrac{1}{3}\sqrt{Rg}$
(B) $\sqrt{Rg}$
(C) $\dfrac{4}{3}\sqrt{Rg}$
(D) $\dfrac{2}{3}\sqrt{Rg}$

Q25·PhysicsSingle correctJEE Main 2025

A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical circle of radius ‘R’ under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is

n\sqrt{gR}

, where

n\ge 1

, then ratio of kinetic energy of the body at bottom to that at top of the circle is

(A) $\dfrac{n}{n+4}$
(B) $\dfrac{n+4}{n}$
(C) $\dfrac{n^2}{n^2+4}$
(D) $\dfrac{n^2+4}{n^2}$

Q26·PhysicsSingle correctJEE Main 2025

A body of mass 4 kg is placed on a plane at a point P having coordinate (3, 4) m. Under the action of force

\vec{F}=(2\hat{i}+3\hat{j})

N, it moves to a new point Q having coordinates (6, 10) m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:

(A)13 : 6
(B)6 : 13
(C)1 : 2
(D)4 : 3

Q27·PhysicsSingle correctJEE Main 2025

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In a central force field, the work done is independent of the path. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below

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

Q28·PhysicsSingle correctJEE Main 2025

A bead of mass "m" slides without friction on the wall of a vertical circular hoop of radius "R" as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is "R". If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes "R", would be (spring constant is "k", g is acceleration due to gravity)

(A) $\sqrt{2gR+\frac{kR^2}{m}}$
(B) $\sqrt{2Rg+\frac{4kR^2}{m}}$
(C) $\sqrt{2Rg+\frac{kR^2}{m}}$
(D) $\sqrt{3Rg+\frac{kR^2}{m}}$

Q29·PhysicsSingle correctJEE Main 2025

A force

F=\alpha+\beta x^2

acts on an object in the x-direction. The work done by the force is 5J when the object is displaced by 1 m. If the constant

\alpha=1

N then β will be

(A)15 N/m $^2$
(B)10 N/m $^2$
(C)12 N/m $^2$
(D)8 N/m $^2$

Q30·PhysicsSingle correctJEE Main 2025

A force

\vec{F}=2\hat{i}+b\hat{j}+\hat{k}

is applied on a particle and it undergoes a displacement

\hat{i}-2\hat{j}-\hat{k}

. What will be the value of b, if work done on the particle is zero.

(A)0
(B) $\frac{1}{2}$
(C) $\frac{1}{3}$
(D)2

Q31·PhysicsSingle correctJEE Main 2025

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is: (Take acceleration due to gravity as 10 m/s

^2

)

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

Q32·PhysicsSingle correctJEE Main 2025

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical circular motion. Initially, by applying horizontal velocity v_a at the lowest point A, the string becomes slack at the topmost point D. The ratio of the kinetic energy of the bob at the points B and C (shown in the figure, at heights l/2 and 3l/2 above A) is:

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

Q33·PhysicsNumericalJEE Main 2024

A force

(3x^{2}+2x-5)

N displaces a body from

x=2

m to

x=4

m. Work done by this force is _______ J.

Q34·PhysicsSingle correctJEE Main 2024

A stationary particle breaks into two parts of masses

m_A

and

m_B

which move with velocities

v_A

and

v_B

respectively. The ratio of their kinetic energies

(K_B:K_A)

is:

(A) $v_B:v_A$
(B) $m_B:m_A$
(C) $m_B v_B:m_A v_A$
(D) $1:1$

Q35·PhysicsSingle correctJEE Main 2024

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is:

(A) $\sqrt{6}$ m
(B) $2$ m
(C) $1$ m
(D) $\sqrt{5}$ m

Q36·PhysicsSingle correctJEE Main 2024

Three bodies

A

,

B

and

C

have equal kinetic energies and their masses are

400\,g

,

1.2\,kg

and

1.6\,kg

respectively. The ratio of their linear momenta is:

(A) $1:\sqrt3:2$
(B) $1:\sqrt3:\sqrt2$
(C) $\sqrt2:\sqrt3:1$
(D) $\sqrt3:\sqrt2:1$

Q37·PhysicsSingle correctJEE Main 2024

A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is:

(A) $32\%$
(B) $44\%$
(C) $16\%$
(D) $84\%$

Q38·PhysicsSingle correctJEE Main 2024

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

(A)500%
(B)600%
(C)6%
(D)60%

Q39·PhysicsSingle correctJEE Main 2024

Four particles

A

,

B

,

C

,

D

of mass

\tfrac{m}{2}

,

m

,

2m

,

4m

have the same momentum, respectively. The particle with maximum kinetic energy is:

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

Q40·PhysicsSingle correctJEE Main 2024

A body of mass 50 kg is lifted to a height of 20 m from the ground in two different ways as shown in the figures. The ratio of the work done against gravity in the two respective cases will be:

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

Q41·PhysicsSingle correctJEE Main 2024

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time

t

is proportional to:

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

Q42·PhysicsSingle correctJEE Main 2024

If a rubber ball falls from a height

h

and rebounds upto the height of

h/2

. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are:

(A) $50\%,\ \sqrt{\dfrac{gh}{2}}$
(B) $50\%,\ \sqrt{gh}$
(C) $40\%,\ \sqrt{2gh}$
(D) $50\%,\ \sqrt{2gh}$

Q43·PhysicsSingle correctJEE Main 2024

A body of

m

kg slides from rest along the curve of vertical circle from point A to B in friction less path (shown in the figure). The velocity of the body at B is (given,

R=14

m,

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

and

\sqrt{2}=1.4

)

(A)19.8 m/s
(B)21.9 m/s
(C)16.7 m/s
(D)10.6 m/s

Q44·PhysicsSingle correctJEE Main 2024

A simple pendulum of length

1\,m

has a wooden bob of mass

1\,kg

. It is struck by a bullet of mass

10^{-2}\,kg

moving with a speed of

2\times10^2\,m/s

. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use

g=10\,m/s^2

)

(A) $0.30\,m$
(B) $0.20\,m$
(C) $0.35\,m$
(D) $0.40\,m$

Q45·PhysicsSingle correctJEE Main 2024

An artillery piece of mass

M_1

fires a shell of mass

M_2

horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :

(A) $\dfrac{M_1}{(M_1+M_2)}$
(B) $\dfrac{M_2}{M_1}$
(C) $\dfrac{M_2}{(M_1+M_2)}$
(D) $\dfrac{M_1}{M_2}$

Q46·PhysicsSingle correctJEE Main 2024

A body of mass 2 kg begins to move under the action of a time dependent force given by

\vec{F}=\left(6t\,\hat{i}+6t^2\,\hat{j}\right)

N. The power developed by the force at the time

t

is given by

(A) $\left(6t^4+9t^5\right)$ W
(B) $\left(3t^3+6t^5\right)$ W
(C) $\left(9t^5+6t^3\right)$ W
(D) $\left(9t^3+6t^5\right)$ W

Q47·PhysicsSingle correctJEE Main 2024

A block of mass 1 kg is pushed up a surface inclined at angle

60^\circ

by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is: [

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

]

(A) $5\sqrt{3}$ J
(B)5 J
(C) $5\times 10^3$ J
(D)10 J

Q48·PhysicsSingle correctJEE Main 2024

A particle is placed at the point

A

of a frictionless track

ABC

as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point

B

is: (Take

g=10\,m/s^2

)

(A) $20\,m/s$
(B) $\sqrt{10}\,m/s$
(C) $2\sqrt{10}\,m/s$
(D) $10\,m/s$

Q49·PhysicsSingle correctJEE Main 2024

The potential energy function (in J) of a particle in a region of space is given as

U=(2x^2+3y^3+2z)

. Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point

P(1,2,3)

m is :

(A) $2$
(B) $6$
(C) $4$
(D) $8$

Q50·PhysicsSingle correctJEE Main 2024

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use

g=10

ms

^{-2}

]

(A) $6\sqrt{5}$ ms $^{-1}$
(B) $5\sqrt{6}$ ms $^{-1}$
(C) $5\sqrt{5}$ ms $^{-1}$
(D) $2\sqrt{5}$ ms $^{-1}$

Q51·PhysicsSingle correctJEE Main 2024

A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies

\dfrac{(K.E.)_{A}}{(K.E.)_{B}}

is:

(A)3 : 2
(B)5 : 1
(C)2 : 5
(D)1 : 5

Q52·PhysicsSingle correctJEE Main 2024

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (in J) is :

(A) $4200$
(B) $3900$
(C) $4000$
(D) $4500$

Q53·PhysicsSingle correctJEE Main 2024

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is:

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

Q54·PhysicsNumericalJEE Main 2023

A block of mass

10

kg is moving along x-axis under the action of force

F = 5x

N. The work done by the force in moving the block from

x = 2

m to

4

m will be __________ J.

Q55·PhysicsNumericalJEE Main 2023

A car accelerates from rest to u m/s. The energy spent in this process is E J. The energy required to accelerate the car from u m/s to 2u m/s is nE J. The value of n is ____.

Q56·PhysicsSingle correctJEE Main 2023

Two bodies are having kinetic energies in the ratio

16:9

. If they have same linear momentum, the ratio of their masses respectively is:

(A) $4:3$
(B) $3:4$
(C) $16:9$
(D) $9:16$

Q57·PhysicsSingle correctJEE Main 2023

The ratio of powers of two motors is

\dfrac{3\sqrt x}{\sqrt x+1}

, that are capable of raising

300\,kg

of water in

5

minutes and

50\,kg

of water in

2

minutes respectively from a well of

100\,m

deep. The value of

x

will be:

(A) $2$
(B) $4$
(C) $2.4$
(D) $16$

Q58·PhysicsNumericalJEE Main 2023

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _________ kJ. [The coefficient of friction between tyre of bus and road is 0.04]

Q59·PhysicsNumericalJEE Main 2023

A force

\vec{F} = (2 + 3x)\hat{i}

acts on a particle in the x direction where F is in newton and x is in meter. The work done by this force during a displacement from

x = 0

to

x = 4

m, is ____ J.

Q60·PhysicsNumericalJEE Main 2023

A block of mass

5

kg starting from rest is pulled up on a smooth inclined plane making an angle of

30^\circ

with the horizontal with an effective acceleration of

1

ms

^{-2}

. The power delivered by the pulling force at

t=10

s from the start is ____ W. [Use

g=10

ms

^{-2}

] (calculate the nearest integer value)

Q61·PhysicsNumericalJEE Main 2023

A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fits inside the tube. The speed of block is 22 m/s when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is _________ J. [Given

g=10

m/s

^2

]

Q62·PhysicsNumericalJEE Main 2023

The maximum load carried by an elevator is

1400

kg (

600

kg passengers +

800

kg elevator), which is moving up with a uniform speed of

3

ms

^{-1}

, and the frictional force acting on it is

2000

N. The maximum power used by the motor is _______ kW (

g=10

m/s

^2

).

Q63·PhysicsSingle correctJEE Main 2023

A bullet of mass 0.1 kg moving horizontally with speed 400 ms

^{-1}

hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is ____. (Given

g=10

m/s

^2

)

(A)0.50
(B)0.90
(C)0.65
(D)0.25

Q64·PhysicsNumericalJEE Main 2023

A body of mass 5 kg is moving with a momentum of 10 kg ms

^{-1}

. A force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the kinetic energy of the body is ____ J.

Q65·PhysicsNumericalJEE Main 2023

The momentum of a body is increased by

50\%

. The percentage increase in the kinetic energy of the body is ______

\%

Q66·PhysicsNumericalJEE Main 2023

A particle of mass

10\,g

moves in a straight line with retardation

2x

, where

x

is the displacement in SI units. Its loss of kinetic energy for above displacement is

\left(\dfrac{10}{x}\right)^{-n}\,J

. The value of

n

is _____.

Q67·PhysicsNumericalJEE Main 2023

A body is dropped on ground from a height '

h_1

' and after hitting the ground, it rebounds to a height '

h_2

'. If the ratio of velocities of the body just before and after hitting ground is 4, then percentage loss in kinetic energy of the body is

\dfrac{x}{4}

. The value of

x

is

Q68·PhysicsNumericalJEE Main 2023

A small particle moves to position

5\hat{i}-2\hat{j}+\hat{k}

from its initial position

2\hat{i}+3\hat{j}-4\hat{k}

under the action of force

5\hat{i}+2\hat{j}+7\hat{k}

N. The value of work done will be _______ J.

Q69·PhysicsNumericalJEE Main 2023

A force

F=(5+3y^2)

acts on a particle in the

y

-direction, where F is in newton and

y

is in meter. The work done by the force during a displacement from

y=2

m to

y=5

m is _________ J.

Q70·PhysicsNumericalJEE Main 2023

A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is

\dfrac{1}{3}\alpha^{2}\sqrt{\dfrac{2P}{m}}

. The value of

\alpha

will be _______.

Q71·PhysicsSingle correctJEE Main 2023

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be:

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

(A) $0$
(B) $4$ m/s
(C) $2$ m/s
(D) $0.25$ m/s

Q72·PhysicsNumericalJEE Main 2023

A 0.4 kg mass takes 8 s to reach the ground when dropped from a certain height '

P

' above the surface of earth. The loss of potential energy in the last second of fall is ________ J. (Take

g = 10

m/s

^2

)

Q73·PhysicsSingle correctJEE Main 2023

Identify the correct statements from the following: A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. C. Work done by friction on a body sliding down an inclined plane is positive. D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero. E. Work done by air resistance on an oscillating pendulum is negative. Choose the correct answer from the options given below:

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

Q74·PhysicsNumericalJEE Main 2023

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ______

\text{ms}^{-1}

Q75·PhysicsNumericalJEE Main 2023

An object of mass '

m

' initially at rest on a smooth horizontal plane starts moving under the action of force

F=2

N. In the process of its linear motion, the angle

\theta

between the direction of force and horizontal varies as

\theta=kx

, where

k

is constant and

x

is the distance covered by the object from the initial position. The expression of kinetic energy of the object will be

E=\dfrac{n}{k}\sin\theta

. The value of

n

is _______.

Q76·PhysicsNumericalJEE Main 2023

A body of mass

1

kg begins to move under the action of a time dependent force

\vec F=(t\hat i+3t^2\hat j)

N, where

\hat i

and

\hat j

are the unit vectors along

x

and

y

axis. The power developed by above force, at the time

t=2

s, will be _________ W.

Q77·PhysicsSingle correctJEE Main 2022

If momentum of a body is increased by 20%, then its kinetic energy increases by :

(A)36%
(B)40%
(C)44%
(D)48%

Q78·PhysicsSingle correctJEE Main 2022

A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is

(A)45 m
(B)90 m
(C)125 m
(D)25 m

Q79·PhysicsNumericalJEE Main 2022

A block of mass 'm' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be nE Nm

^{-1}

for n = ________.

Q80·PhysicsSingle correctJEE Main 2022

Two cylindrical vessels of equal cross-sectional area 16 cm

^{2}

contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water = 10

^{3}

kg/m

^{3}

and g = 10 ms

^{-2}

]

(A)0.25 J
(B)1 J
(C)8 J
(D)12 J

Q81·PhysicsSingle correctJEE Main 2022

Sand is being dropped from a stationary dropper at a rate of 0.5 kgs

^{-1}

on a conveyor belt moving with a velocity of 5 ms

^{-1}

. The power needed to keep belt moving with the same velocity will be :

(A)1.25 W
(B)2.5 W
(C)6.25 W
(D)12.5 W

Q82·PhysicsSingle correctJEE Main 2022

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be :

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

Q83·PhysicsSingle correctJEE Main 2022

As per the given figure, two blocks each of mass 250g are connected to a spring of spring constant 2Nm

^{-1}

. If both are given velocity v in opposite directions, then maximum elongation of the spring is :

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

Q84·PhysicsSingle correctJEE Main 2022

A body of mass 0.5 kg travels on straight line path with velocity

v = (3x^{2} + 4)

m/s. The net workdone by the force during its displacement from

x = 0

to

x = 2

m is :

(A)64 J
(B)60 J
(C)120 J
(D)128 J

Q85·PhysicsSingle correctJEE Main 2022

In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when it reaches point 'B' is :

(A) $\frac{1}{2}mg\,y_0^2$
(B) $\frac{1}{2}mg\,y^2$
(C) $mg(y - y_0)$
(D) $mgy_0$

Q86·PhysicsSingle correctJEE Main 2022

A particle of mass 500 gm is moving in a straight line with velocity

\upsilon = b\,x^{5/2}

. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25

m^{-3/2}

s^{-1}

).

(A)2 J
(B)4 J
(C)8 J
(D)16 J

Q87·PhysicsSingle correctJEE Main 2022

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms

^{-1}

enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by

F = -kx

where k = 12 Nm

^{-1}

. The speed of the block as it just crosses the rough surface will be:

(A)Zero
(B)1.5 ms $^{-1}$
(C)2.0 ms $^{-1}$
(D)2.5 ms $^{-1}$

Q88·PhysicsNumericalJEE Main 2022

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then. the trolly car starts moving with velocity 2 ms

^{-1}

. The velocity of the running man was ______________ ms

^{-1}

. when he jumps into the car.

Q89·PhysicsSingle correctJEE Main 2022

Water fall from a 40 m high dam at the rate of

9\times10^4

kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100W lamps, that can be lit, is: (Take g = 10 ms

^{-2}

)

(A)25
(B)50
(C)100
(D)18

Q90·PhysicsNumericalJEE Main 2022

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60° with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be ______________ ms

^{-1}

. (if g = 10 m/s

^{2}

)

Q91·PhysicsSingle correctJEE Main 2022

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as

a = k^{2}rt^{2}

. where k is a constant. The power delivered to the particle by the force acting on it is given as

(A)zero
(B) $mk^{2}r^{2}t^{2}$
(C) $mk^{2}r^{2}t$
(D) $mk^{2}rt$

Q92·PhysicsSingle correctJEE Main 2022

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)

(A)50.0%
(B)66.6%
(C)55.5%
(D)33.3%

Q93·PhysicsNumericalJEE Main 2022

A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed

\frac{v}{3}

and the bob just completes the vertical circle. The value of v is ________

ms^{-1}

. (if g = 10

m/s^{2}

)

Q94·PhysicsSingle correctJEE Main 2022

Arrange the four graphs in descending order of total work done; where

W_1

,

W_2

,

W_3

and

W_4

are the work done corresponding to figure a, b, c and d respectively.

(A) $W_3 > W_2 > W_1 > W_4$
(B) $W_3 > W_2 > W_4 > W_1$
(C) $W_2 > W_3 > W_4 > W_1$
(D) $W_2 > W_3 > W_1 > W_4$

Q95·PhysicsNumericalJEE Main 2022

A 0.5 kg block moving at a speed of

12\ \mathrm{ms}^{-1}

compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be __________

\mathrm{Nm}^{-1}

.

Q96·PhysicsSingle correctJEE Main 2022

Potential energy as a function of r is given by

U = \dfrac{A}{r^{10}} - \dfrac{B}{r^{5}}

, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

(A) $\left(\dfrac{A}{B}\right)^{\frac{1}{5}}$
(B) $\left(\dfrac{B}{A}\right)^{\frac{1}{5}}$
(C) $\left(\dfrac{2A}{B}\right)^{\frac{1}{5}}$
(D) $\left(\dfrac{B}{2A}\right)^{\frac{1}{5}}$

Q97·PhysicsNumericalJEE Main 2022

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance

\dfrac{h}{2}

. The spring constant is ________ Nm

^{-1}

. (Use g = 10 ms

^{-2}

)

Q98·PhysicsSingle correctJEE Main 2022

A particle experiences a variable force

\vec{F}=(4x\hat{i}+3y^{2}\hat{j})

in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, the Kinetic Energy changes by

(A)50.0 J
(B)12.5 J
(C)25.0 J
(D)0 J

Q99·PhysicsNumericalJEE Advanced 2021

A pendulum consists of a bob of mass

m

= 0.1 kg and a massless inextensible string of length

L

= 1.0 m. It is suspended from a fixed point at height

H

= 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse

P

= 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is

J

kg-m

^2

/s. The kinetic energy of the pendulum just after the lift-off is

K

Joules. The value of

K

is ____.

Q100·PhysicsNumericalJEE Main 2021

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh

^{-1}

when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is .......... × 10

^{5}

N/m.

Q101·PhysicsSingle correctJEE Main 2021

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of

0.8\sqrt{gh}

. The value of workdone by the air-friction is :

(A)–0.68 mgh
(B)mgh
(C)1.64 mgh
(D)0.64 mgh

Q102·PhysicsNumericalJEE Main 2021

A block moving horizontally on a smooth surface with a speed of 40 ms

^{-1}

splits into two equal parts. If one of the parts moves at 60 ms

^{-1}

in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = _______.

Q103·PhysicsSingle correctJEE Main 2021

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-

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

Q104·PhysicsSingle correctJEE Main 2021

A body of mass M moving at speed

V_{0}

collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles

\theta_{1}

and

\theta_{2}

with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles

\theta_{1}

and

\theta_{2}

will be equal, is :

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

Q105·PhysicsNumericalJEE Main 2021

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45

^\circ

and 60

^\circ

with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is

\frac{1}{\sqrt{x}}

. The value of x is ....... .

Q106·PhysicsNumericalJEE Main 2021

A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = _____ m/s so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m/s

^{2}

)

Q107·PhysicsNumericalJEE Main 2021

A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is ........... . (Take

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

)

Q108·PhysicsSingle correctJEE Main 2021

Three objects A, B and c are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 and 2 m respectively. A moves towards B with a speed of 9m / s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. all motions occur along same straight line. The final speed of C is :

(A)4 m /s
(B)6 m /s
(C)9 m /s
(D)3 m /s

Q109·PhysicsSingle correctJEE Main 2021

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservation force F(x) acts on it. Suppose that

E_{mech}

= 8J, the incorrect statement for this system is : [ where K.E. = kinetic energy]

(A)at x = x $_3$ , K.E. = 4J.
(B)at x > x $_4$ , K.E. is constant throughout the region .
(C)at x < x $_1$ , K.E. is smallest and the particle is moving at the slowest speed.
(D)at x = x $_2$ , K.E. is greatest and the particle is moving at the fastest speed.

Q110·PhysicsSingle correctJEE Main 2021

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

(A) $\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$
(B) $\left(\frac{9P}{8m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$
(C) $\left(\frac{9m}{8P}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$
(D) $\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{2}{3}}$

Q111·PhysicsNumericalJEE Main 2021

A body of mass 2 kg moving with a speed of 4 m /s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is

\frac{x}{10}

m / s. Then the value of x is ___________.

Q112·PhysicsNumericalJEE Main 2021

A pendulum bob has a speed of 3 m / s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60° to the vertical will be

\left(g = 10m/s^2\right)

__________ m/s.

Q113·PhysicsNumericalJEE Main 2021

A force of

F = (5y + 20)\hat{j}

N acts on a particle. The work done by this force when the particle is moved from y = 0m to y = 10m is ________ J.

Q114·PhysicsSingle correctJEE Main 2021

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase.

\left(\text{take } g=9.8\,\mathrm{ms^{-2}}\right)

(A) $-627.2$ J
(B) $-62720.0$ J
(C) $+627.2$ J
(D)784.0 J

Q115·PhysicsSingle correctJEE Main 2021

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :

(A) $t^{\frac{3}{4}}$
(B) $t^{\frac{3}{2}}$
(C) $t^{\frac{1}{2}}$
(D) $t^{\frac{1}{4}}$

Q116·PhysicsSingle correctJEE Main 2021

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be :

(A)100%
(B)200%
(C)400%
(D)300%

Q117·PhysicsNumericalJEE Main 2021

In a spring gun having spring constant 100 N / m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground . The value of d is ____________ m.

Q118·PhysicsNumericalJEE Main 2021

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s

^{2}

) The value of 'x' to the nearest integer is_____.

Q119·PhysicsSingle correctJEE Main 2021

An object of mass

m_1

collides with another object of mass

m_2

, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses

m_2 : m_1

is :

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

Q120·PhysicsSingle correctJEE Main 2021

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-

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

Q121·PhysicsNumericalJEE Main 2021

A ball of mass 4 kg, moving with a velocity of 10 ms

^{-1}

, collides with a spring of length 8 m and force constant 100 Nm

^{-1}

. The length of the compressed spring is x m. The value of x, to the nearest integer, is_____.

Q122·PhysicsSingle correctJEE Main 2021

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20

ms^{-1}

. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now ?

(A)19.0 $ms^{-1}$
(B)4.47 $ms^{-1}$
(C)14.41 $ms^{-1}$
(D)1.00 $ms^{-1}$

Q123·PhysicsNumericalJEE Main 2021

A ball of mass 10 kg moving with a velocity

10\sqrt{3}

ms

^{-1}

along X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to the X-axis. The configuration of pieces after collision is shown in the figure. The value of θ to the nearest integer is _______.

Q124·PhysicsSingle correctJEE Main 2021

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is : (Take g = 9.8 ms

^{-2}

)

(A)841.4 m/s
(B)811.4 m/s
(C)831.4 m/s
(D)821.4 m/s

Q125·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 : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m<<M, body 'Q' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

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

Q126·PhysicsNumericalJEE Main 2021

Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2. The value of n will be_____.

Q127·PhysicsNumericalJEE Main 2021

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as

U = \dfrac{\alpha}{r^{10}} - \dfrac{\beta}{r^5} - 3

Where, a and b are positive constants. The equilibrium distance between two atoms will

\left(\dfrac{2\alpha}{\beta}\right)^{\frac{a}{b}}

. Where a = ________

Q128·PhysicsNumericalJEE Main 2021

A ball with a speed of 9 m/s collides with another identical ball at rest. After thecollision, the direction of each ball makes an angle of 30° with the original direction. The ratio of velocities of the balls after collision is x : y, where x is ___________.

Q129·PhysicsNumericalJEE Main 2021

Two solids A and B of mass 1 kg and 2 kg respectively are moving withequal linear momentum. The ratio of their kinetic energies (K.E.)

_{A}

: (K.E.)

_{B}

will be

\dfrac{A}{1}

. So the value of A will be _________.

Q130·PhysicsMultiple correctJEE Advanced 2020

A student skates up a ramp that makes an angle

30^\circ

with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed

v_0

and wants to turn around over a semicircular path xyz of radius

R

during which he/she reaches a maximum height

h

(at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

(A) $v_0^2 - 2gh = \frac{1}{2}gR$
(B) $v_0^2 - 2gh = \frac{\sqrt{3}}{2}gR$
(C)the centripetal force required at points x and z is zero
(D)the centripetal force required is maximum at points x and z

Q131·PhysicsNumericalJEE Main 2020

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is __________.

Q132·PhysicsNumericalJEE Main 2020

A body of mass 2 kg, is driven by an engine delivering, a constant power 1 J/s. the body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) __________.

Q133·PhysicsSingle correctJEE Main 2020

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

(A)5250 J
(B)5690 J
(C)3280 J
(D)2780 J

Q134·PhysicsSingle correctJEE Main 2020

Blocks of masses m, 2m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of 'p' is close to:

(A)77
(B)37
(C)87
(D)94

Q135·PhysicsSingle correctJEE Main 2020

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement(s) – time (t) graph that describes the motion of the particle is (graph are drawn schematically and are not to scale):

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

Q136·PhysicsNumericalJEE Main 2020

A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is (g = 10

ms^{-2}

) __________.

Q137·PhysicsSingle correctJEE Main 2020

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the combined system strikes the floor, is [Take g = 10 m/s

^{2}

. Assume there is no rotational motion and loss of energy after the collision is negligible.]

(A)21 J
(B)20 J
(C)23 J
(D)19 J

Q138·PhysicsSingle correctJEE Main 2020

Consider a force

\vec{F}=-x\hat{i}+y\hat{j}

. The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is: (all quantities are in SI units)

(A)2
(B) $\dfrac{1}{2}$
(C)1
(D) $\dfrac{3}{2}$

Q139·PhysicsSingle correctJEE Main 2020

Two particles of equal mass 'm' have respective initial velocities u

\hat{i}

and u

\left(\dfrac{\hat{i}+\hat{j}}{2}\right)

. They collide completely inelastically. The energy lost in the process is:

(A) $\dfrac{1}{3}m u^{2}$
(B) $\dfrac{1}{8}m u^{2}$
(C) $\sqrt{\dfrac{2}{3}}m u^{2}$
(D) $\dfrac{3}{4}m u^{2}$

Q140·PhysicsSingle correctJEE Main 2020

A particle of mass m is projected with a speed u form the ground at an angle

\theta = \frac{\pi}{3}

w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity

u\hat{i}

. The horizontal distance covered by the combined mass before reaching the ground is:

(A) $\frac{5}{8}\frac{u^{2}}{g}$
(B) $\frac{3\sqrt{2}}{4}\frac{u^{2}}{g}$
(C) $\frac{3\sqrt{3}}{8}\frac{u^{2}}{g}$
(D) $2\sqrt{2}\frac{u^{2}}{g}$

Q141·PhysicsSingle correctJEE Main 2020

A particle of mass m is dropped from a height h above the ground. At the same time another particle of same mass is thrown vertically upwards from the ground with a speed of

\sqrt{2gh}

. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of

\sqrt{\dfrac{h}{g}}

is:

(A) $\dfrac{1}{2}$
(B) $\sqrt{\dfrac{1}{2}}$
(C) $\sqrt{\dfrac{3}{4}}$
(D) $\sqrt{\dfrac{3}{2}}$

Q142·PhysicsNumericalJEE Main 2020

A body A, of mass m = 0.1 kg has an initial velocity of

3\hat{i}

ms

^{-1}

. It collides elastically with another body, B of the same mass which has an initial velocity of

5\hat{j}

ms

^{-1}

. After collision, A moves with a velocity

\vec{v} = 4(\hat{i} + \hat{j})

. The energy of B after collision is written as

\dfrac{x}{10}

J. The value of x is ___________.

Q143·PhysicsSingle correctJEE Main 2020

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. the frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s

^2

) must be at least:

(A)56300 W
(B)66000 W
(C)62360 W
(D)48000 W

Q144·PhysicsNumericalJEE Main 2020

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest of a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it leading its highest point P(height 1 m) the kinetic energy of the particle (in J) is: (Figure drawn is schematic and not to scale (take g = 10 ms

^{-2}

)

Q145·PhysicsSingle correctJEE Main 2020

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to: (1 HP = 746 W, g = 10 ms

^{-2}

)

(A)1.5 ms $^{-1}$
(B)2.0 ms $^{-1}$
(C)1.7 m/s $^{-1}$
(D)1.9 m/s $^{-1}$

Q146·PhysicsNumericalJEE Advanced 2019

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force

\vec{F} = \left(\alpha y\hat{i} + 2\alpha x\hat{j}\right) N

, where x and y are in meter and α = – 1

Nm^{-1}

. The work done on the particle by this force

\vec{F}

will be ________ Joule.

Q147·PhysicsSingle correctJEE Main 2019

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude

\theta_0

. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance

\ell

(

\ell

<< L), is close to :

(A) $Mg\ell(1+\theta_0^{2})$
(B) $Mg\ell(1-\theta_0^{2})$
(C) $Mg\ell$
(D) $Mg\ell\left(1+\dfrac{\theta_0^{2}}{2}\right)$

Q148·PhysicsSingle correctJEE Main 2019

A bullet of mass 20 g has an initial speed of 1 ms

^{-1}

just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistances of

2.5 \times 10^{-2}

N, the speed of the bullet after emerging from the other side of the wall is close to

(A)0.7 ms $^{-1}$
(B)0.3 ms $^{-1}$
(C)0.1 ms $^{-1}$
(D)0.4 ms $^{-1}$

Q149·PhysicsSingle correctJEE Main 2019

A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:

(A) $\dfrac{2v^{2}}{7g}$
(B) $\dfrac{v^{2}}{g}$
(C) $\dfrac{2v^{2}}{5g}$
(D) $\dfrac{v^{2}}{2g}$

Q150·PhysicsSingle correctJEE Main 2019

A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its

\left(\frac{1}{n}\right)^{th}

part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

(A)nMgL
(B) $\frac{MgL}{2n^2}$
(C) $\frac{2MgL}{n^2}$
(D) $\frac{MgL}{n^2}$

Q151·PhysicsSingle correctJEE Main 2019

A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

(A)1.5 kg
(B)1.2 kg
(C)1.8 kg
(D)1.0 kg

Q152·PhysicsSingle correctJEE Main 2019

A body of mass m

_1

moving with an unknown velocity of

v_1\hat{i}

undergoes a collinear collision with a body of mass m

_2

moving with a velocity

v_2\hat{i}

. After collision m

_1

and m

_2

move with velocities of

v_3\hat{i}

and

v_4\hat{i}

respectively. If m

_2

= 0.5 m

_1

and v

_3

= 0.5 v

_1

then v

_1

is:

(A) $v_4 - \frac{v_2}{2}$
(B) $v_4 - \frac{v_2}{4}$
(C) $v_4 - v_2$
(D) $v_4 + v_2$

Q153·PhysicsSingle correctJEE Main 2019

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:

(A)2.5 J
(B)4 J
(C)5 J
(D)6.5 J

Q154·PhysicsSingle correctJEE Main 2019

A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle

\theta_0

. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle

\theta_1

. Then M is given by:

(A) $\dfrac{m}{2}\left(\dfrac{\theta_0+\theta_1}{\theta_0-\theta_1}\right)$
(B) $m\left(\dfrac{\theta_0-\theta_1}{\theta_0+\theta_1}\right)$
(C) $m\left(\dfrac{\theta_0+\theta_1}{\theta_0-\theta_1}\right)$
(D) $\dfrac{m}{2}\left(\dfrac{\theta_0-\theta_1}{\theta_0+\theta_1}\right)$

Q155·PhysicsSingle correctJEE Main 2019

An alpha-particle of mass m suffers 1-deminsional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is :

(A)2 m
(B)3.5 m
(C)1.5 m
(D)4 m

Q156·PhysicsSingle correctJEE Main 2019

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms

^{-1}

, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is: (g = 10 ms

^{-2}

)

(A)20 m
(B)30 m
(C)40 m
(D)10 m

Q157·PhysicsSingle correctJEE Main 2019

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time t is:

(A) $-\dfrac{mg^{2}t^{2}}{8}$
(B) $\dfrac{mg^{2}t^{2}}{8}$
(C)0
(D) $\dfrac{3mg^{2}t^{2}}{8}$

Q158·PhysicsSingle correctJEE Main 2019

A force acts on a 2 kg object so that its position is given as a function of time as

x = 3t^{2} + 5

. What is the work done by this force in first 5 seconds?

(A)850 J
(B)950 J
(C)875 J
(D)900 J

Q159·PhysicsSingle correctJEE Advanced 2018

In the List-I below, four different paths of a particle are given as functions of time. In these functions,

\alpha

and

\beta

are positive constants of appropriate dimensions and

\alpha \neq \beta

. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned:

\vec{p}

is the linear momentum,

\vec{L}

is the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

LIST-I	LIST-II
P. $\vec{r}(t) = \alpha t\,\hat{i} + \beta t\,\hat{j}$	1. $\vec{p}$
Q. $\vec{r}(t) = \alpha \cos \omega t\,\hat{i} + \beta \sin \omega t\,\hat{j}$	2. $\vec{L}$
R. $\vec{r}(t) = \alpha(\cos \omega t\,\hat{i} + \sin \omega t\,\hat{j})$	3.K
S. $\vec{r}(t) = \alpha t\,\hat{i} + \dfrac{\beta}{2}t^{2}\,\hat{j}$	4.U
	5.E

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

Q160·PhysicsMultiple correctJEE Advanced 2018

The potential energy of a particle of mass

m

at a distance

r

from a fixed point

O

is given by

V(r) = kr^{2}/2

, where

k

is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius

R

about the point

O

. If

v

is the speed of the particle and

L

is the magnitude of its angular momentum about

O

, which of the following statements is (are) true?

(A) $v = \sqrt{\frac{k}{2m}}\,R$
(B) $v = \sqrt{\frac{k}{m}}\,R$
(C) $L = \sqrt{mk}\,R^{2}$
(D) $L = \sqrt{\frac{mk}{2}}\,R^{2}$

Q161·PhysicsMultiple correctJEE Advanced 2018

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as

dK/dt = \gamma t

, where

\gamma

is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

(A)The force applied on the particle is constant
(B)The speed of the particle is proportional to time
(C)The distance of the particle from the origin increases linearly with time
(D)The force is conservative

Q162·PhysicsMatrix matchJEE Advanced 2015

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (

a

and

U_{0}

are constants). Match the potential energies in column I to the corresponding statement(s) in column II.

Column I	Column II
A. $U_{1}(x) = \dfrac{U_{0}}{2}\left[1 - \left(\dfrac{x}{a}\right)^{2}\right]^{2}$	P.The force acting on the particle is zero at $x = a$ .
B. $U_{2}(x) = \dfrac{U_{0}}{2}\left(\dfrac{x}{a}\right)^{2}$	Q.The force acting on the particle is zero at $x = 0$ .
C. $U_{3}(x) = \dfrac{U_{0}}{2}\left(\dfrac{x}{a}\right)^{2}\exp\left[-\left(\dfrac{x}{a}\right)^{2}\right]$	R.The force acting on the particle is zero at $x = -a$ .
D. $U_{4}(x) = \dfrac{U_{0}}{2}\left[\dfrac{x}{a} - \dfrac{1}{3}\left(\dfrac{x}{a}\right)^{3}\right]$	S.The particle experiences an attractive force towards $x = 0$ in the region $\|x\| < a$ .
	T.The particle with total energy $\dfrac{U_{0}}{4}$ can oscillate about the point $x = -a$ .

Q163·PhysicsIntegerJEE Advanced 2014

Consider an elliptically shaped rail

PQ

in the vertical plane with

OP = 3 \text{ m}

and

OQ = 4 \text{ m}

. A block of mass

1 \text{ kg}

is pulled along the rail from

P

to

Q

with a force of

18 \text{ N}

, which is always parallel to line

PQ

(see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches

Q

is

(n \times 10)

Joules. The value of

n

is (take acceleration due to gravity

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

)

Q164·PhysicsSingle correctJEE Advanced 2014

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy

K

with time

t

most appropriately? The figures are only illustrative and not to the scale.

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

Q165·PhysicsSingle correctJEE Advanced 2014

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

(A)always radially outwards.
(B)always radially inwards.
(C)radially outwards initially and radially inwards later.
(D)radially inwards initially and radially outwards later.

Q166·PhysicsIntegerJEE Advanced 2013

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is

Q167·PhysicsIntegerJEE Advanced 2013

A bob of mass m, suspended by a string of length

l_{1}

is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length

l_{2}

, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio

l_{1}/l_{2}

is

Q168·PhysicsSingle correctJEE Advanced 2013

A small block of mass

1\ \mathrm{kg}

is released from rest at the top of a rough track. The track is circular arc of radius

40\ \mathrm{m}

. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is

150\ \mathrm{J}

. (Take the acceleration due to gravity,

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

). The speed of the block when it reaches the point Q is

(A) $5\ \mathrm{ms^{-1}}$
(B) $10\ \mathrm{ms^{-1}}$
(C) $10\sqrt{3}\ \mathrm{ms^{-1}}$
(D) $20\ \mathrm{ms^{-1}}$

Q169·PhysicsSingle correctJEE Advanced 2013

The work done on a particle of mass

m

by a force

K\left[\frac{x}{(x^{2}+y^{2})^{3/2}}\hat{i}+\frac{y}{(x^{2}+y^{2})^{3/2}}\hat{j}\right]

(K being a constant of appropriate dimensions), when the particle is taken from the point

(a, 0)

to the point

(0, a)

along a circular path of radius

a

about the origin in the x-y plane is

(A) $\frac{2K\pi}{a}$
(B) $\frac{K\pi}{a}$
(C) $\frac{K\pi}{2a}$
(D)0

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