How many questions from Laws of Motion appear in JEE?

Laws of Motion has appeared in 130 of the last 186 JEE Main and JEE Advanced papers — about 70% of them — contributing 196 questions in total across those papers.

Is Laws of Motion an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 70% 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 Laws of Motion 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.

Laws of Motion JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Main 2026

A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take

g = 10

m/s

^2

)

(A) $\tan^{-1}(0.5)$
(B) $\tan^{-1}(0.75)$
(C) $\tan^{-1}(1.125)$
(D) $\tan^{-1}(0.25)$

Q2·PhysicsSingle correctJEE Main 2026

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take g

= 10

m/s

^{2}

)

(A)7.74
(B)7.20
(C)6.55
(D)4.50

Q3·PhysicsNumericalJEE Main 2026

A block takes

t

time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time

\frac{t}{2}

to slide down the plane. The coefficient of friction between the block and the inclined plane is

\left(\frac{\alpha}{100}\right)

. The value of

\alpha

is __________.

Q4·PhysicsSingle correctJEE Main 2026

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient friction μ. The cube (S) moves towards the right with acceleration of

\frac{g}{2}

, where g is gravitational acceleration. During this movement the block P and Q remain stationary. The value of μ is ________. (take g = 10 m/s²)

(A)0.33
(B)0.67
(C)1
(D)0.5

Q5·PhysicsSingle correctJEE Main 2026

Three masses

m_1 = 4

kg,

m_2 = 4

kg and

m_3 = 6

kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of

T_1/T_2

is ______. (take

g = 10

m/s

^2

)

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

Q6·PhysicsSingle correctJEE Main 2026

A wedge

Y

with mass of 10 kg and all frictionless surfaces and the inclined surface making 37° with horizontal. A block

X

with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At

t = 0

wedge

(Y)

is pulled toward right with constant force

(f)

of 24 N. Taking the block

X

at rest at

t = 0

, the time taken by it to slide down 8.8 m on the slope, while

Y

is on the move, is ______ s. (take

\tan(37°) = 3/4

and

g = 10

m/s

^2

)

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

Q7·PhysicsSingle correctJEE Main 2026

The time taken by a block of mass

m

to slide down from the highest point to the lowest point on a rough inclined plane is 50% more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at

45^\circ

with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _____.

(A) $3/4$
(B) $2/3$
(C) $5/9$
(D) $4/9$

Q8·PhysicsSingle correctJEE Main 2026

At

t = 0

, a body of mass 100 g starts moving under the influence of a force

(5\hat{i} + 10\hat{j})

N. After 2 s its position is

(2x\hat{i} + 5y\hat{j})

m. The ratio

x : y

is ______.

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

Q9·PhysicsSingle correctJEE Main 2026

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is ______. (Take

g = 10

m/s

^{2}

)

(A)0.1
(B)0.5
(C)0.7
(D)0.3

Q10·PhysicsSingle correctJEE Main 2026

A block of mass 5 kg is moving on an inclined plane which makes an angle of 30° with the horizontal. Friction coefficient between the block and inclined plane surface is

\frac{\sqrt{3}}{2}

. The force to be applied on the block so that the block will move down without acceleration is _____ N.

(A)25
(B)12.5
(C)7.5
(D)15

Q11·PhysicsSingle correctJEE Main 2026

A particle of mass m falls from rest through a resistive medium having resistive force, F = –kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time(t) ?

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

Q12·PhysicsSingle correctJEE Main 2026

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration

a_0

. The angle between the inclined plane and ground is θ and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is _________.

(A) $\sqrt{\dfrac{2L}{g\sin 2\theta - a_0(1 + \cos 2\theta)}}$
(B) $\sqrt{\dfrac{4L}{g\sin 2\theta - a_0(1 + \cos 2\theta)}}$
(C) $\sqrt{\dfrac{4L}{g\cos^2 \theta - a_0 \sin\theta\cos\theta}}$
(D) $\sqrt{\dfrac{2L}{g\sin \theta - a_0 \cos\theta}}$

Q13·PhysicsNumericalJEE Main 2026

In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force

\vec{F}

required to slide the block C with constant speed is _________ N. (Used

g = 10

m/s

^{2}

)

Q14·PhysicsSingle correctJEE Main 2026

A flexible chain of mass

m

hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is

30^\circ

. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is _____.

(A) $\frac{\sqrt{3}}{2}mg$
(B) $\frac{1}{2}mg$
(C) $mg$
(D) $\sqrt{3}\,mg$

Q15·PhysicsSingle correctJEE Main 2026

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is_____m/s.

(A) $10\sqrt{2}$
(B) $12\sqrt{2}$
(C)12
(D) $24\sqrt{2}$

Q16·PhysicsSingle correctJEE Main 2026

A block is sliding down on an inclined plane of slope θ and at an instant

t = 0

this block is given an upward momentum so that it starts moving up on the inclined surface with velocity

u

. The distance

(S)

travelled by the block before its velocity become zero, is______. (g = gravitational acceleration)

(A) $\frac{u^{2}}{4g\sin\theta}$
(B) $\frac{2u^{2}}{g\cos\theta}$
(C) $\frac{u^{2}}{\sqrt{2}g\cos\theta}$
(D) $\frac{u^{2}}{2g\cos\theta}$

Q17·PhysicsSingle correctJEE Main 2026

A 4 kg mass moves under the influence of a force

\vec{F} = (4t^{3}\hat{i} - 3t\hat{j})

N where t is the time in second. If mass starts from origin at t = 0, the velocity and position after t = 2s will be :

(A) $\vec{v} = 3\hat{i} + \frac{3}{2}\hat{j}$ $\vec{r} = \frac{6}{5}\hat{i} + \hat{j}$
(B) $\vec{v} = 4\hat{i} - \frac{3}{2}\hat{j}$ $\vec{r} = \frac{8}{5}\hat{i} - \hat{j}$
(C) $\vec{v} = 4\hat{i} + \frac{5}{2}\hat{j}$ $\vec{r} = \frac{8}{5}\hat{i} + 2\hat{j}$
(D) $\vec{v} = 4\hat{i} - \frac{3}{2}\hat{j}$ $\vec{r} = \frac{6}{5}\hat{i} - \hat{j}$

Q18·PhysicsSingle correctJEE Main 2026

A large drum having radius R is spinning around its axis with angular velocity

\omega

, as shown in figure. The minimum value of

\omega

so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is

\mu

, is :

(A) $\sqrt{\dfrac{\mu\text{g}}{\text{R}}}$
(B) $\sqrt{\dfrac{2\text{g}}{\mu\text{R}}}$
(C) $\sqrt{\dfrac{\text{g}}{2\mu\text{R}}}$
(D) $\sqrt{\dfrac{\text{g}}{\mu\text{R}}}$

Q19·PhysicsNumericalJEE Advanced 2025

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height y (in m ) of the elevator, from the ground, with time t (in s) is given by

y = 8\left[1 + \sin\left(\frac{2\pi t}{T}\right)\right]

, where T = 40

\pi

s. Taking acceleration due to gravity, g = 10

\text{m/s}^{2}

, the maximum variation of the object's weight (in N ) as observed in the experiment is _____

Q20·PhysicsSingle correctJEE Main 2025

A body of mass 2 kg moving with velocity

\vec v_{in}=3\hat i+4\hat j\ ms^{-1}

enters into a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of

\dfrac{5}{3}

seconds, then velocity of the body when it emerges from force field is:

(A) $4\hat i+3\hat j+5\hat k$
(B) $3\hat i+4\hat j+5\hat k$
(C) $3\hat i+4\hat j-5\hat k$
(D) $3\hat i+4\hat j+\sqrt5\,\hat k$

Q21·PhysicsSingle correctJEE Main 2025

An object with mass 500 g moves along x-axis with speed

v=4\sqrt{x}

m/s. The force acting on the object is:

(A)8 N
(B)5 N
(C)6 N
(D)4 N

Q22·PhysicsSingle correctJEE Main 2025

A cubic block of mass

m

is sliding down on an inclined plane at

60^\circ

with an acceleration of

\dfrac{g}{2}

, the value of coefficient of kinetic friction is

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

Q23·PhysicsSingle correctJEE Main 2025

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle

45^\circ

with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is: (work done by the applied force)

(A)970 J
(B)735 J
(C)245 J
(D)490 J

Q24·PhysicsSingle correctJEE Main 2025

A body of mass

m

is suspended by two strings making angles

\theta_1

and

\theta_2

with the horizontal ceiling with tensions

T_1

and

T_2

simultaneously.

T_1

and

T_2

are related by

T_1=\sqrt{3}\,T_2

. The angles

\theta_1

and

\theta_2

are

(A) $\theta_1=30^\circ$ , $\theta_2=60^\circ$ with $T_2=\dfrac{3mg}{4}$
(B) $\theta_1=60^\circ$ , $\theta_2=30^\circ$ with $T_2=\dfrac{mg}{2}$
(C) $\theta_1=45^\circ$ , $\theta_2=45^\circ$ with $T_2=\dfrac{3mg}{4}$
(D) $\theta_1=30^\circ$ , $\theta_2=60^\circ$ with $T_2=\dfrac{4mg}{5}$

Q25·PhysicsSingle correctJEE Main 2025

A body of mass 1 kg is suspended with the help of two strings making angles as shown in the figure. Magnitude of tensions

T_1

and

T_2

, respectively, are (in N):

(A) $5,\ 5\sqrt3$
(B) $5\sqrt3,\ 5$
(C) $5\sqrt3,\ 5\sqrt3$
(D) $5,\ 5$

Q26·PhysicsSingle correctJEE Main 2025

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e.

\dfrac{dm}{dt}\propto\sqrt{v}

. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

(A) $P^2\propto v^3$
(B) $P\propto\sqrt{v}$
(C) $P\propto v$
(D) $P^2\propto v^5$

Q27·PhysicsSingle correctJEE Main 2025

A balloon and its content having mass M is moving up with an acceleration 'a'. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be: (Take 'g' as acceleration due to gravity)

(A) $\frac{3Ma}{2a-g}$
(B) $\frac{3Ma}{2a+g}$
(C) $\frac{2Ma}{3a+g}$
(D) $\frac{2Ma}{3a-g}$

Q28·PhysicsSingle correctJEE Main 2025

A car of mass ‘m’ moves on a banked road having radius ‘r’ and banking angle θ. To avoid slipping from banked road, the maximum permissible speed of the car is

v_0

. The coefficient of friction μ between the wheels of the car and the banked road is :-

(A) $\dfrac{v_0^2+rg\tan\theta}{rg-v_0^2\tan\theta}$
(B) $\dfrac{v_0^2+rg\tan\theta}{rg+v_0^2\tan\theta}$
(C) $\dfrac{v_0^2-rg\tan\theta}{rg+v_0^2\tan\theta}$
(D) $\dfrac{v_0^2-rg\tan\theta}{rg-v_0^2\tan\theta}$

Q29·PhysicsIntegerJEE Main 2025

A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes

\left(\dfrac{3}{\pi}\right)

rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML.

Q30·PhysicsNumericalJEE Main 2024

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is

1\times10^{11}\ \mathrm{N\ m^{-2}}

. Original length of the wire is 2 m and the area of cross section is

2\ \mathrm{cm^{2}}

. The wire will extend in length by ______

\mu

m.

Q31·PhysicsSingle correctJEE Main 2024

A light unstretchable string passing over a smooth light pulley connects two blocks of masses

m_1

and

m_2

. If the acceleration of the system is

\dfrac{g}{8}

, then the ratio of the masses

\dfrac{m_2}{m_1}

is:

(A)9 : 7
(B)4 : 3
(C)5 : 3
(D)8 : 1

Q32·PhysicsSingle correctJEE Main 2024

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they will move:

(A)In opposite directions with speed in the ratio of 1:2 respectively
(B)In opposite directions with speed in the ratio of 2:1 respectively
(C)In the same direction with same speed
(D)In opposite directions with speed in the ratio of 3:2 respectively

Q33·PhysicsSingle correctJEE Main 2024

A 1 kg mass is suspended from the ceiling by a rope of length 4 m. A horizontal force

F

is applied at the mid point of the rope so that the rope makes an angle of

45^{\circ}

with respect to the vertical axis as shown in the figure. The magnitude of

F

is: (use

g=10

m/s

^{2}

)

(A) $\dfrac{10}{\sqrt{2}}$ N
(B)1 N
(C) $\dfrac{1}{10\sqrt{2}}$ N
(D)10 N

Q34·PhysicsSingle correctJEE Main 2024

A given object takes

n

times the time to slide down a 45° rough inclined plane as it takes to slide down an identical perfectly smooth 45° inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is:

(A) $1-\dfrac{1}{n^2}$
(B) $1-n^2$
(C) $\sqrt{1-\dfrac{1}{n^2}}$
(D) $\dfrac{1}{\sqrt{1-n^2}}$

Q35·PhysicsSingle correctJEE Main 2024

A player caught a cricket ball of mass

150\,g

moving at a speed of

20\,m/s

. If the catching process is completed in

0.1\,s

, the magnitude of force exerted by the ball on the hand of the player is:

(A) $150\,N$
(B) $3\,N$
(C) $30\,N$
(D) $300\,N$

Q36·PhysicsSingle correctJEE Main 2024

A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking

30^\circ

. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely : (

g = 10

m/s

^2

,

\sqrt{3} = 1.73

)

(A)70.4 m/s
(B)51.4 m/s
(C)264 m/s
(D)102.8 m/s

Q37·PhysicsSingle correctJEE Main 2024

A light string passing over a smooth light pulley connects two blocks of masses

m_{1}

and

m_{2}

(where

m_{2}>m_{1}

). If the acceleration of the system is

\tfrac{g}{\sqrt{2}}

, then the ratio of the masses

\tfrac{m_{1}}{m_{2}}

is:

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

Q38·PhysicsSingle correctJEE Main 2024

A body of weight 200 N is suspended form a tree branch thought a chain of mass 10 kg. The branch pulls the chain by a force equal to (if

g = 10

m/s

^2

):

(A)150 N
(B)300 N
(C)200 N
(D)100 N

Q39·PhysicsSingle correctJEE Main 2024

A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on top of the block, the floor yields and the block and cylinder together go down with an acceleration of

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

. The action force of the system on the floor is equal to:

(A)297 N
(B)294 N
(C)291 N
(D)196 N

Q40·PhysicsSingle correctJEE Main 2024

A heavy box of mass 50 kg is moving on a horizontal surface. If the coefficient of kinetic friction between the box and the horizontal surface is 0.3, then the force of kinetic friction is: (Take

g=9.8

m/s

^2

)

(A)14.7 N
(B)147 N
(C)1.47 N
(D)1470 N

Q41·PhysicsSingle correctJEE Main 2024

A particle moves in the x-y plane under the influence of a force

\vec{F}

such that its linear momentum is

\vec{P}(t)=\hat{i}\cos(kt)-\hat{j}\sin(kt)

. If

k

is constant, the angle between

\vec{F}

and

\vec{P}

will be:

(A) $\dfrac{\pi}{2}$
(B) $\dfrac{\pi}{6}$
(C) $\dfrac{\pi}{4}$
(D) $\dfrac{\pi}{3}$

Q42·PhysicsNumericalJEE Main 2024

Three blocks

M_1

,

M_2

,

M_3

of masses 4 kg, 6 kg and 10 kg respectively hang from a smooth pulley using ropes 1, 2 and 3 in succession (rope 1 at the top carries all three, rope 2 carries

M_2

and

M_3

, rope 3 carries

M_3

). The tension

T_1

in rope 1 when they move upward with acceleration

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

is ___ N (with

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

).

Q43·PhysicsNumericalJEE Main 2024

Two forces

\vec F_1

and

\vec F_2

are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between

\vec F_1

and

\vec F_2

is

\cos^{-1}\left(\dfrac1n\right)

. The value of

|n|

is ___

Q44·PhysicsSingle correctJEE Main 2024

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time

t

. Which of the following curve best describes acceleration of the block with time

t

:

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

Q45·PhysicsSingle correctJEE Main 2024

A 2 kg brick begins to slide over a surface which is inclined at an angle of

45^{\circ}

with respect to horizontal axis. The co-efficient of static friction between their surfaces is

(A)1
(B) $\tfrac{1}{\sqrt{3}}$
(C)0.5
(D) $\tfrac{1}{\sqrt{2}}$

Q46·PhysicsSingle correctJEE Main 2024

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):

(A)24
(B)12
(C)25
(D)30

Q47·PhysicsSingle correctJEE Main 2024

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is

0.04

, the acceleration of the system in

m/s^2

is: (Consider that the masses are massless and unstretchable and the pulley is also massless and frictionless)

(A) $3$
(B) $4$
(C) $2$
(D) $1.2$

Q48·PhysicsSingle correctJEE Main 2024

A ball of mass

0.5\,kg

is attached to a string of length

50\,cm

. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is

400\,N

. The maximum possible value of angular velocity of the ball in rad/s, is:

(A) $1600$
(B) $40$
(C) $1000$
(D) $20$

Q49·PhysicsSingle correctJEE Main 2024

A body of mass 4 kg experiences two forces

\vec F_1=5\hat i+8\hat j+7\hat k

and

\vec F_2=3\hat i-4\hat j-3\hat k

. The acceleration acting on the body is:

(A) $-2\hat i-\hat j-\hat k$
(B) $4\hat i+2\hat j+2\hat k$
(C) $2\hat i+\hat j+\hat k$
(D) $2\hat i+3\hat j+3\hat k$

Q50·PhysicsSingle correctJEE Main 2024

A coin is placed on a disc. The coefficient of friction between the coin and the disc is

\mu

. If the distance of the coin from the center of the disc is r, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

(A) $\dfrac{\mu g}{r}$
(B) $\sqrt{\dfrac{r}{\mu g}}$
(C) $\sqrt{\dfrac{\mu g}{r}}$
(D) $\dfrac{\mu}{\sqrt{rg}}$

Q51·PhysicsSingle correctJEE Main 2024

A light string passing over a smooth light fixed pulley connects two blocks of masses

m_1

and

m_2

. If the acceleration of the system is

\dfrac{g}{8}

, then the ratio of masses is

(A) $\dfrac{9}{7}$
(B) $\dfrac{8}{1}$
(C) $\dfrac{4}{3}$
(D) $\dfrac{5}{3}$

Q52·PhysicsSingle correctJEE Main 2024

In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for which M = 10 kg will move down with an acceleration of 2 m/s

^2

, is : (take

g=10

m/s

^2

and

\tan 37^\circ=3/4

)

(A)9 kg
(B)4.5 kg
(C)6.5 kg
(D)2.25 kg

Q53·PhysicsSingle correctJEE Main 2024

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions

T_1

and

T_2

in the string are respectively:

(A)40N, 64N
(B)60N, 80N
(C)88N, 96N
(D)80N, 100N

Q54·PhysicsSingle correctJEE Main 2024

A spherical body of mass

100\,g

is dropped from a height of

10\,m

from the ground. After hitting the ground, the body rebounds to a height of

5\,m

. The impulse of force imparted by the ground to the body is given by: (given

g=9.8\,m/s^2

)

(A) $4.32\,kg\,ms^{-1}$
(B) $43.2\,kg\,ms^{-1}$
(C) $23.32\,kg\,ms^{-1}$
(D) $2.39\,kg\,ms^{-1}$

Q55·PhysicsSingle correctJEE Main 2024

A block of mass

m

is placed on a surface having vertical cross section given by

y=\dfrac{x^2}{4}

. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

(A) $\dfrac{1}{4}$ m
(B) $\dfrac{1}{2}$ m
(C) $\dfrac{1}{6}$ m
(D) $\dfrac{1}{3}$ m

Q56·PhysicsSingle correctJEE Main 2024

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass

2\,kg

is:

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

Q57·PhysicsSingle correctJEE Main 2024

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, in order to have constant centripetal force, their velocities will be in the ratio of

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

Q58·PhysicsSingle correctJEE Main 2024

A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if

\pi^{2}=9.8

and

g=9.8

m/s

^{2}

):

(A)97 N
(B)9.8 N
(C)8.82 N
(D)17.8 N

Q59·PhysicsNumericalJEE Main 2024

A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at

t=0

is 4 m/s, the time taken to complete the first revolution will be

\dfrac{1}{\alpha}\left[1-e^{-2\pi}\right]

s, where

\alpha=

___.

Q60·PhysicsSingle correctJEE Main 2024

Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. 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

Q61·PhysicsSingle correctJEE Main 2024

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given,

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

):

(A)6.0 cm
(B)5.4 cm
(C)4.8 cm
(D)4.2 cm

Q62·PhysicsSingle correctJEE Main 2024

A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:

(A)6
(B)2
(C)3
(D)5

Q63·PhysicsSingle correctJEE Main 2024

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle

60^\circ

with the horizontal, the weight experienced by the man is :

(A)6 kg
(B)12 kg
(C)3 kg
(D) $6\sqrt3$ kg

Q64·PhysicsSingle correctJEE Main 2023

A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of 0.2 rad/s. The centripetal force acting on the vehicle is:

(A)560 N
(B)2800 N
(C)14 N
(D)2240 N

Q65·PhysicsSingle correctJEE Main 2023

A bullet

10\,g

leaves the barrel of gun with a velocity of

600\,m/s

. If the barrel of gun is

50\,cm

long and mass of gun is

3\,kg

, then value of impulse supplied to the gun will be:

(A) $12\,Ns$
(B) $6\,Ns$
(C) $36\,Ns$
(D) $3\,Ns$

Q66·PhysicsSingle correctJEE Main 2023

Given below are two statements: Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. Statement II: A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given 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 correct but II not explanation of I
(D)Both Statement I and Statement II are correct

Q67·PhysicsSingle correctJEE Main 2023

Three forces

F_1=10

N,

F_2=8

N,

F_3=6

N are acting on a particle of mass 5 kg. The forces

F_2

and

F_3

are applied perpendicular so that particle remains at rest. If the force

F_1

is removed, then the acceleration of the particle is:

(A)2 ms $^{-2}$
(B)0.5 ms $^{-2}$
(C)4.8 ms $^{-2}$
(D)7 ms $^{-2}$

Q68·PhysicsSingle correctJEE Main 2023

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is:

(A)5
(B)50
(C)100
(D)25

Q69·PhysicsSingle correctJEE Main 2023

A body of mass

500

g moves along the x-axis such that its velocity varies with displacement x according to the relation

v=10\sqrt{x}

m/s. The force acting on the body is:

(A) $166$ N
(B) $25$ N
(C) $125$ N
(D) $5$ N

Q70·PhysicsSingle correctJEE Main 2023

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of _____ from the centre:

(A)2 cm
(B)1 cm
(C)8 cm
(D)4 cm

Q71·PhysicsSingle correctJEE Main 2023

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity

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

Q72·PhysicsSingle correctJEE Main 2023

At any instant the velocity of a particle of mass

500

g is

(2t\,\hat{i} + 3t^{2}\,\hat{j})

ms

^{-1}

. If the force acting on the particle at

t = 1

s is

(\hat{i} + x\hat{j})

N. Then the value of

x

will be:

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

Q73·PhysicsSingle correctJEE Main 2023

A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be

(A) $80\ N$
(B) $50\ N$
(C) $100\ N$
(D) $40\ N$

Q74·PhysicsSingle correctJEE Main 2023

A block of mass

5

kg is placed at rest on a table of rough surface. Now, if a force of

30

N is applied in the direction parallel to surface of the table, the block slides through a distance of

50

m in an interval of time

10

s. Coefficient of kinetic friction is (given,

g=10

ms

^{-2}

):

(A) $0.60$
(B) $0.25$
(C) $0.75$
(D) $0.50$

Q75·PhysicsSingle correctJEE Main 2023

Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure.

(A)Fig (c)
(B)Fig (b)
(C)Fig (d)
(D)Fig (a)

Q76·PhysicsSingle correctJEE Main 2023

A block of mass

10

kg lying on a horizontal surface is pulled by a force F acting at an angle

30°

with horizontal. For

\mu_s=0.25

, the block will just start to move for the value of F: [Given

g=10

ms

^{-2}

]

(A) $20$ N
(B) $33.3$ N
(C) $25.2$ N
(D) $35.7$ N

Q77·PhysicsSingle correctJEE Main 2023

100

balls each of mass

m

moving with speed

v

simultaneously strike a wall normally and reflected back with same speed, in time

t

sec. The total force exerted by the balls on the wall is

(A) $\frac{100mv}{t}$
(B) $200mvt$
(C) $\frac{mv}{100t}$
(D) $\frac{200mv}{t}$

Q78·PhysicsSingle correctJEE Main 2023

A body of mass

10

kg is moving with an initial speed of

20

m/s. The body stops after

5

s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity

g=10~ms^{-2}

)

(A) $0.3$
(B) $0.5$
(C) $0.2$
(D) $0.4$

Q79·PhysicsSingle correctJEE Main 2023

As shown in figure, a

70

kg garden roller is pushed with a force of

\vec{F}=200

N at an angle of

30^\circ

with horizontal. The normal reaction on the roller is (Given

g=10

m s

^{-2}

)

(A) $800\sqrt{2}$ N
(B) $200\sqrt{3}$ N
(C) $600$ N
(D) $800$ N

Q80·PhysicsNumericalJEE Main 2023

A ball is dropped from a height of

20

m. If the coefficient of restitution for the collision between ball and floor is

0.5

, after hitting the floor, the ball rebounds to a height of _________ m.

Q81·PhysicsNumericalJEE Main 2023

A lift of mass

M = 500

kg is descending with speed of

2\,\text{ms}^{-1}

. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of

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

. The kinetic energy of the lift at the end of fall through to a distance of

6

m will be __________ kJ.

Q82·PhysicsSingle correctJEE Main 2023

A ball of mass

200

g rests on a vertical post of height

20

m. A bullet of mass

10

g, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance

30

m and the bullet at a distance of

120

m from the foot of the post. The value of initial velocity of the bullet will be (if

g=10\,m/s^2

):

(A) $360$ m/s
(B) $400$ m/s
(C) $60$ m/s
(D) $120$ m/s

Q83·PhysicsSingle correctJEE Main 2023

A block of

\sqrt{3}

kg is attached to a string whose other end is attached to the wall. An unknown horizontal force F is applied so that the string makes an angle of

30^{\circ}

with the wall. The tension T is: (Given

g=10

ms

^{-2}

)

(A) $20$ N
(B) $10$ N
(C) $15$ N
(D) $25$ N

Q84·PhysicsSingle correctJEE Main 2023

A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 m s

^{-1}

each. The recoil velocity of the gun is:

(A) $1.5$ m/s
(B) $0.6$ m/s
(C) $2.5$ m/s
(D) $0.02$ m/s

Q85·PhysicsSingle correctJEE Main 2023

The figure represents the momentum time (p-t) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively? If

(t_3-t_2)<t_1

(A)c and b
(B)b and c
(C) $a$ and $b$
(D)c and a

Q86·PhysicsNumericalJEE Main 2023

A stone tied to a 180 cm long string at its end is making 28 revolutions in a horizontal circle in every minute. The magnitude of acceleration of the stone is

\dfrac{1936}{x}

ms

^{-2}

. The value of

x

is _______. (Take

\pi=\dfrac{22}{7}

)

Q87·PhysicsSingle correctJEE Main 2023

A force acts for

20\,s

on a body of mass

20\,kg

, starting from rest, after which the force ceases and then body describes

50\,m

in the next

10\,s

. The value of force will be:

(A) $40\,N$
(B) $5\,N$
(C) $20\,N$
(D) $10\,N$

Q88·PhysicsSingle correctJEE Main 2023

The time taken by an object to slide down

45^\circ

rough inclined plane is

n

times as it takes to slide down a perfectly smooth

45^\circ

incline plane. The coefficient of kinetic friction between the object and the incline plane is:

(A) $\sqrt{1-\dfrac{1}{n^2}}$
(B) $1+\dfrac{1}{n^2}$
(C) $1-\dfrac{1}{n^2}$
(D) $\sqrt{\dfrac{1}{1-n^2}}$

Q89·PhysicsSingle correctJEE Main 2023

A block of mass

m

slides down the plane inclined at angle

30^\circ

with an acceleration

\dfrac{g}{4}

. The value of coefficient of kinetic friction will be:

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

Q90·PhysicsSingle correctJEE Main 2023

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if friction between tyres and road is 0.34. [take

g = 10

ms

^{-2}

]

(A)17 ms $^{-1}$
(B)13 ms $^{-1}$
(C)22.4 ms $^{-1}$
(D)3.4 ms $^{-1}$

Q91·PhysicsSingle correctJEE Main 2023

Consider a block kept on an inclined plane (inclined at

45^\circ

) as shown in the figure. If the force required to just push it up the incline is

2

times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (

\mu

) is equal to:

(A) $0.25$
(B) $0.50$
(C) $0.60$
(D) $0.33$

Q92·PhysicsSingle correctJEE Main 2023

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take

g=10

m/s

^2

)

(A) $\dfrac{\pi}{3}$
(B) $\dfrac{\pi}{2}$
(C) $\dfrac{\pi}{4}$
(D) $\dfrac{\pi}{6}$

Q93·PhysicsNumericalJEE Main 2023

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is _______ N.

Q94·PhysicsSingle correctJEE Main 2023

A body of mass

200

g is tied to a spring of spring constant

12.5

N/m, while the other end of spring is fixed at point

O

. If the body moves about

O

in a circular path on a smooth horizontal surface with constant angular speed

5

rad/s, then the ratio of extension in the spring to its natural length will be:

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

Q95·PhysicsSingle correctJEE Main 2023

As shown in the figure, a weightless pulley

P

is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if

g=10

m/s

^2

):

(A) $(4\sqrt{3}+1)$ N
(B) $4(\sqrt{3}+1)$ N
(C) $(4\sqrt{3}-1)$ N
(D) $4(\sqrt{3}-1)$ N

Q96·PhysicsSingle correctJEE Main 2023

Given below are two statements: Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. 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

Q97·PhysicsNumericalJEE Main 2022

A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity

x\sqrt{F}

rad s

^{-1}

. If F be the force exerted by the liquid at the other end then the value of x will be ______.

Q98·PhysicsSingle correctJEE Main 2022

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v) ?

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

Q99·PhysicsSingle correctJEE Main 2022

Two bodies of masses

m_1 = 5

kg and

m_2 = 3

kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass

m_1

will be :[Take

g = 10

ms

^{-2}

]

(A)30 N
(B)40 N
(C)50 N
(D)60 N

Q100·PhysicsSingle correctJEE Main 2022

In two different experiments, an object of mass 5 kg moving with a speed of 25 ms

^{-1}

hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

(A)Impulse and average force acting on the object will be same for both the cases.
(B)Impulse will be same for both the cases but the average force will be different.
(C)Average force will be same for both the cases but the impulse will be different.
(D)Average force and impulse will be different for both the cases.

Q101·PhysicsSingle correctJEE Main 2022

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length '

l

' is hanging on one side and rest of its length 'L

-

l

' is hanging on the other side of the pulley. At a certain point of time, when

l = \dfrac{L}{x}

, the acceleration of the chain is

\dfrac{g}{2}

. The value of x is ………

(A)6
(B)2
(C)1.5
(D)4

Q102·PhysicsSingle correctJEE Main 2022

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

(A)3
(B)9
(C)12
(D)18

Q103·PhysicsSingle correctJEE Main 2022

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be :

(A)Mg
(B)Mg cos θ
(C) $\sqrt{Mg\sin\theta + Mg\cos\theta}$
(D) $Mg\sin\theta\sqrt{1 + \mu}$

Q104·PhysicsSingle correctJEE Main 2022

A block 'A' takes 2 s to slide down a frictionless incline of 30° and length '

l

', kept inside a lift going up with uniform velocity '

v

'. If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately:

(A)2.66 s
(B)0.83 s
(C)1.68 s
(D)0.70 s

Q105·PhysicsNumericalJEE Main 2022

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is

t\left(\sqrt{2} + 1\right)

s. The value of t is……..(use g = 10 m/s

^{2}

)

Q106·PhysicsSingle correctJEE Main 2022

A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag is 0.4 Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take g = 10 m/s

^{-2}

]

(A)2 m
(B)0.5 m
(C)3.2 m
(D)0.8 ms

Q107·PhysicsSingle correctJEE Main 2022

A ball of mass 0.15 kg hits the wall with its initial speed of 12

\text{ms}^{-1}

and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N. calculate the time duration of the contact of ball with the wall.

(A)0.018 s
(B)0.036 s
(C)0.009 s
(D)0.072 s

Q108·PhysicsSingle correctJEE Main 2022

Three masses M = 100 kg, m

_{1}

= 10 kg and m

_{2}

=20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m

_{2}

moves upward with an acceleration of 2 ms

^{-2}

. The value of F is : (Take g = 10 ms

^{-2}

)

(A)3360 N
(B)3380 N
(C)3120 N
(D)3240 N

Q109·PhysicsSingle correctJEE Main 2022

Two masses

M_1

and .

M_2

are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass

M_2

is twice that of

M_1

. the acceleration of the system is

a_1

. When the mass

M_2

is thrice that of

M_1

. The acceleration of The system is

a_2

. The ratio

\frac{a_1}{a_2}

will be:

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

Q110·PhysicsSingle correctJEE Main 2022

A monkey of mass 50kg climbs on a rope which can withstand the tension (T) of 350N. If monkey initially climbs down with an acceleration of 4m/s

^{2}

and then climbs up with an acceleration of 5m/s

^{2}

. Choose the correct option (g = 10m/s

^{2}

)

(A)T = 700N while climbing upward
(B)T = 350 N while going downward
(C)Rope will break while climbing upward
(D)Rope will break while going downward

Q111·PhysicsNumericalJEE Main 2022

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force

F_1

to

F_2

is 1 : x where x = _______ .

Q112·PhysicsSingle correctJEE Main 2022

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30

ms^{-1}

and 40

ms^{-1}

respectively. The velocity of the third piece will be :

(A)15 $ms^{-1}$
(B)25 $ms^{-1}$
(C)35 $ms^{-1}$
(D)50 $ms^{-1}$

Q113·PhysicsSingle correctJEE Main 2022

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1

kgs^{-1}

and at a speed of 10

ms^{-1}

. Then, the initial acceleration of the block, in

ms^{-2}

, will be :

(A)3
(B)6
(C)5
(D)4

Q114·PhysicsSingle correctJEE Main 2022

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is. (Given

g = 10\ \mathrm{ms}^{-2}

.)

(A) $1\ \mathrm{ms}^{-2}$
(B) $1/5\ \mathrm{ms}^{-2}$
(C) $4/5\ \mathrm{ms}^{-2}$
(D) $8/11\ \mathrm{ms}^{-2}$

Q115·PhysicsSingle correctJEE Main 2022

A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of 'a' will be :

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

Q116·PhysicsNumericalJEE Main 2022

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement. as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation. tension in the string is

\frac{x}{5}

Mg for x = _________. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)

Q117·PhysicsSingle correctJEE Main 2022

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be :

(A)9.8 N
(B)39.2 N
(C)49 N
(D)78.4 N

Q118·PhysicsSingle correctJEE Main 2022

A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is

\sqrt{x(u^{2}-gL)}

. The value of x is

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

Q119·PhysicsNumericalJEE Main 2022

A mass of 10 kg is suspended vertically by a rope of length 5m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is

\theta = \tan^{-1}(x \times 10^{-1})

. The value of x is _______ . (Given g = 10 m/s

^{2}

)

Q120·PhysicsSingle correctJEE Main 2022

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R ?

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

Q121·PhysicsSingle correctJEE Main 2022

In the arrangement shown in figure

a_1

,

a_2

,

a_3

and

a_4

are the accelerations of masses

m_1

,

m_2

,

m_3

and

m_4

respectively. Which of the following relation is true for this arrangement?

(A) $4a_1 + 2a_2 + a_3 + a_4 = 0$
(B) $a_1 + 4a_2 + 3a_3 + a_4 = 0$
(C) $a_1 + 4a_2 + 3a_3 + 2a_4 = 0$
(D) $2a_1 + 2a_2 + 3a_3 + a_4 = 0$

Q122·PhysicsNumericalJEE Main 2022

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms

^{-1}

. The impulse imparted to the ball is ________________Ns.

Q123·PhysicsSingle correctJEE Main 2022

A person is standing in an elevator. In which situation, he experiences weight loss ?

(A)When the elevator moves upward with constant acceleration
(B)When the elevator moves downward with constant acceleration
(C)When the elevator moves upward with uniform velocity
(D)When the elevator moves downward with uniform velocity

Q124·PhysicsNumericalJEE Main 2022

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the

7^{th}

and

8^{th}

ball is______________N when

6^{th}

ball just leaves the table.

Q125·PhysicsNumericalJEE Main 2022

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force

F = \sqrt{x} N

as shown in figure. The value of x = _________.

Q126·PhysicsNumericalJEE Main 2022

A curved in a level road has a radius 75m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be__ m/s.

Q127·PhysicsNumericalJEE Main 2022

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is __________ m.

Q128·PhysicsNumericalJEE Main 2022

A force on an object of mass 100g is

(10\hat{i} + 5\hat{j})

N. The position of that object at

t = 2

s is

(a\hat{i} + b\hat{j})

m after starting from rest. The value of

\frac{a}{b}

will be _________

Q129·PhysicsSingle correctJEE Main 2022

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity ω. The coefficient of static friction between the bottom of the beaker and the surface of the disc is μ. The beaker will revolve with the disc if :

(A) $R \le \frac{\mu g}{2\omega^2}$
(B) $R \le \frac{\mu g}{\omega^2}$
(C) $R \ge \frac{\mu g}{2\omega^2}$
(D) $R \ge \frac{\mu g}{\omega^2}$

Q130·PhysicsSingle correctJEE Main 2022

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms

^{-1}

. The coefficient of friction between the surface and bock is 0.5. The distance covered by the block before coming to rest is : [use g = 9.8 ms

^{-2}

]

(A)4.9 m
(B)9.8 m
(C)12.5 m
(D)19.6 m

Q131·PhysicsSingle correctJEE Main 2022

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms

^{-2}

]

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

Q132·PhysicsSingle correctJEE Main 2022

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is

\dfrac{K}{\pi}

rev./min. The value of K is : (Assume the string is massless and unstretchable)

(A)400
(B)300
(C)600
(D)800

Q133·PhysicsSingle correctJEE Main 2022

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is :

(A)the same throughout the motion
(B)minimum at the highest position of the circular path
(C)minimum at the lowest position of the circular path
(D)minimum when the rope is in the horizontal position

Q134·PhysicsNumericalJEE Main 2021

When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time αT, where α is a constant greater than 1. The co-efficient of friction between the body and the rough plane is

\frac{1}{\sqrt{x}}\left(\frac{\alpha^{2}-1}{\alpha^{2}}\right)

where x = ..........

Q135·PhysicsSingle correctJEE Main 2021

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile. The correct applied force vs distance graph will be:

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

Q136·PhysicsSingle correctJEE Main 2021

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given m = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

(A) $\frac{4}{3}$ g
(B) $\frac{6}{5}$ g
(C) $\frac{3}{5}$ g
(D) $\frac{2}{3}$ g

Q137·PhysicsNumericalJEE Main 2021

A car is moving on a plane inclined at 30

^\circ

to the horizontal with an acceleration of 10 ms

^{-2}

parallel to the plane upward. A bob is suspended by a string from the roof of the car.The angle in degrees which the string makes with the vertical is_______. (Take g = 10 ms

^{-2}

)

Q138·PhysicsSingle correctJEE Main 2021

Statement :1 If three forces

\vec{F}_1, \vec{F}_2

and

\vec{F}_3

are represented by three sides of a triangle and

\vec{F}_1 + \vec{F}_2 = -\vec{F}_3

, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : II A triangle made up of three forces

\vec{F}_1, \vec{F}_2

and

\vec{F}_3

as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate 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 false
(D)Both Statement-I and Statement-II are true.

Q139·PhysicsSingle correctJEE Main 2021

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s

^{2}

)

(A)0.34 s
(B)0.2 s
(C)0.25 s
(D)0.4 s

Q140·PhysicsNumericalJEE Main 2021

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is .......N. (take

g = 10

ms

^{-2}

)

Q141·PhysicsSingle correctJEE Main 2021

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20

ms^{-2}

. The gases come out at a relative speed of 500

ms^{-1}

with respect to the rocket :[Use g = 10

m/s^{2}

]

(A)6.0 $\times$ $10^{2}$ kg $s^{-1}$
(B)500 kg $s^{-1}$
(C)10 kg $s^{-1}$
(D)60 kg $s^{-1}$

Q142·PhysicsSingle correctJEE Main 2021

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that

r = \frac{L}{\sqrt{2}}

.The speed of particle will be :

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

Q143·PhysicsNumericalJEE Main 2021

A small block slides down from the top of hemisphere of radius R = 3m as shown in the figure. The height ' h' at which the block will lose contact with the surface of the sphere is __________ m. (Assume there is no friction between the block and the hemisphere)

Q144·PhysicsSingle correctJEE Main 2021

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

F = F_0\left[1 - \left(\frac{t - T}{T}\right)^2\right]

Where F

_0

and T are constants. The force acts only for the time interval 2T. The velocity υ of the particle after time 2T is :

(A)F $_0$ T / 3M
(B)2F $_0$ T / M
(C)4F $_0$ T / 3M
(D)F $_0$ T / 2M

Q145·PhysicsSingle correctJEE Main 2021

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :

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

Q146·PhysicsSingle correctJEE Main 2021

A force

\vec{F} = \left(40\hat{i} + 10\hat{j}\right)

N acts on a body of mass 5 kg. If the body starts from rest, its position vector

\vec{r}

at time t

=

10 s, will be :

(A) $\left(100\hat{i} + 100\hat{j}\right)$ m
(B) $\left(400\hat{i} + 100\hat{j}\right)$ m
(C) $\left(400\hat{i} + 400\hat{j}\right)$ m
(D) $\left(100\hat{i} + 400\hat{j}\right)$ m

Q147·PhysicsSingle correctJEE Main 2021

A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms

^{-1}

, the impulse imparted to the gun velocity of recoil of gun are :

(A)0.4 kg ms $^{-1}$ , 0.1 ms $^{-1}$
(B)0.2 kg ms $^{-1}$ , 0.05 ms $^{-1}$
(C)0.4 kg ms $^{-1}$ , 0.05 ms $^{-1}$
(D)0.2 kg ms $^{-1}$ , 0.1 ms $^{-1}$

Q148·PhysicsSingle correctJEE Main 2021

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is ________

\times 10^{3}

kg m / s

^2

. [ Given cos30° = 0.87,

\mu_5

= 0.2 ]

(A)6.96
(B)10.2
(C)12.4
(D)7.2

Q149·PhysicsSingle correctJEE Main 2021

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s

^2

. The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20kg each, is ________ N. [ Take g = 10m / s

^2

and

\mu_s

= 0.2 ]

(A)714
(B)684
(C)716
(D)686

Q150·PhysicsNumericalJEE Main 2021

A body of mass 'm' is launched up on a rough inclined plane making an angle of

30^{\circ}

with the horizontal. The coefficient of friction between the body and plane is

\frac{\sqrt{x}}{5}

if the time of ascent is half of the time of descent. The value of x is ___________.

Q151·PhysicsNumericalJEE Main 2021

A ball of mass 10 kg moving with a velocity

10\sqrt{3}

m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the x-axis. The velocity of the ball moving at 30° with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is _______ .

Q152·PhysicsSingle correctJEE Main 2021

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is : [The coefficient of static friction,

\mu_s

, is 0.4]

(A) $\frac{7}{2}mg$
(B)5 mg
(C) $\frac{mg}{5}$
(D)0

Q153·PhysicsNumericalJEE Main 2021

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is 'x' N. The value of 'x' to the nearest integer is ______ .

Q154·PhysicsNumericalJEE Main 2021

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is

\frac{3}{7}

. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is ______ N. (Round off to the Nearest Integer) [Take g as 9.8 ms

^{-2}

]

Q155·PhysicsNumericalJEE Main 2021

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction

\frac{1}{\sqrt{3}}

. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ___________. (Round off to the Nearest Integer) [Take g = 10 ms

^{-2}

]

Q156·PhysicsNumericalJEE Main 2021

A boy of mass 4 kg is standing on a piece of wood having mass 5kg . If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _________N.(Round off to the Nearest Integer) [Take g = 10 ms

^{-2}

]

Q157·PhysicsSingle correctJEE Main 2021

A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is

\mu_s

, then the magnitude of negative lift

F_L

acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)

(A) $m\left(\frac{v^2}{\mu_s R} + g\right)$
(B) $m\left(\frac{v^2}{\mu_s R} - g\right)$
(C) $m\left(g - \frac{v^2}{\mu_s R}\right)$
(D) $-m\left(g + \frac{v^2}{\mu_s R}\right)$

Q158·PhysicsSingle correctJEE Main 2021

Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh

^{-1}

and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve (g = 9.8 m/s

^{2}

) Statement II : If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius with the speed of 18.5 kmh

^{-1}

without slipping. In the light of the above statements, choose the correct answer from the options given below.

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

Q159·PhysicsNumericalJEE Main 2021

A body of mass 2kg moves under a force of

(2\hat{i} + 3\hat{j} + 5\hat{k})

N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is __________. (Round off to the Nearest Integer)

Q160·PhysicsNumericalJEE Main 2021

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force

\vec{P}

of magnitude 100 N is applied at point A of the frame. Suppose the force is

\vec{P}

resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN. The value of x, to the nearest integer, is ________. [Given : sin(35°) = 0.573, cos(35°) = 0.819 sin(110°) = 0.939, cos(110°) = −0.342 ]

Q161·PhysicsSingle correctJEE Main 2021

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in figure. The coefficient of kinetic friction is μ

_K

. Then, the block's acceleration 'a' is given by : (g is acceleration due to gravity)

(A) $-\frac{F}{m}\cos\theta - \mu_K\left(g - \frac{F}{m}\sin\theta\right)$
(B) $\frac{F}{m}\cos\theta - \mu_K\left(g - \frac{F}{m}\sin\theta\right)$
(C) $\frac{F}{m}\cos\theta - \mu_K\left(g + \frac{F}{m}\sin\theta\right)$
(D) $\frac{F}{m}\cos\theta + \mu_K\left(g - \frac{F}{m}\sin\theta\right)$

Q162·PhysicsSingle correctJEE Main 2021

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is :

(A)0.0314 N
(B)9.859 × 10 $^{-2}$ N
(C)6.28 × 10 $^{-3}$ N
(D)9.859 × 10 $^{-4}$ N

Q163·PhysicsSingle correctJEE Main 2021

Two masses A and B, each of mass M are fixed together by a massless springs. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration ‘a’, than the acceleration of mass B will be:

(A) $\frac{F+Ma}{M}$
(B) $\frac{F-Ma}{M}$
(C) $\frac{Ma-F}{M}$
(D) $\frac{MF}{F+Ma}$

Q164·PhysicsNumericalJEE Main 2021

A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s

^{2}

will be ____________ N. [g =10m/s

^{2}

]

Q165·PhysicsSingle correctJEE Main 2021

An inclined plane making an angle of 30° with horizontal is placed in a uniform horizontal electric field

200\frac{N}{C}

as shown in the figure. A body of mass 1 kg and charge 5mC is allowed to slide down from rest at a height of 1m. If the coefficient of frication is 0.2, find the time taken by the body to reach the bottom.

\left[g = 9.8\,m/s^{2},\ \sin 30^{\circ} = \frac{1}{2};\ \cos 30^{\circ} = \frac{\sqrt{3}}{2}\right]

(A)2.3 s
(B)0.46 s
(C)1.3 s
(D)0.92 s

Q166·PhysicsNumericalJEE Main 2021

As shown in the figure, a block of mass

\sqrt{3}

kg is kept on a horizontal rough surface of coefficient of friction

\frac{1}{3\sqrt{3}}

. The critical force to be applied on the vertical surface as shown at an angle 60° with horizontal such that it does not move, will be 3x. The value of x will be ________. [g=10m/s

^{2}

; sin 60°=

\frac{\sqrt{3}}{2}

; cos 60°=

\frac{1}{2}

]

Q167·PhysicsNumericalJEE Main 2021

A boy pushes a box of mass 2kg with a force

\vec{F} = \left(20\hat{i} + 10\hat{j}\right)

N on a frictionless surface. If the box was initially at rest, then ____________m is displacement along the x-axis after 10 s.

Q168·PhysicsSingle correctJEE Main 2021

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R

^{3}

. Its time period of revolution will be given by :

(A)T ∝ $R^{\frac{5}{2}}$
(B)T ∝ $R^{2}$
(C)T ∝ $R^{\frac{4}{3}}$
(D)T ∝ $R^{\frac{3}{2}}$

Q169·PhysicsNumericalJEE Main 2021

A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the rato 5 : 1. The velocity of the bob at the highest position is ________ m/s. (take g=10

m/s^2

)

Q170·PhysicsNumericalJEE Main 2021

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be ________ N. [g = 10 ms

^{-2}

]

Q171·PhysicsNumericalJEE Main 2021

An inclined plane is bent in such a way that the vertical cross-section is given by

y = \frac{x^2}{4}

where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction

\mu

= 0.5, the maximum height in cm at which a stationary block will not slip downward is ______ cm.

Q172·PhysicsNumericalJEE Advanced 2020

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance

x_R

from the center (50.00 cm) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are 0.40 and 0.32, respectively, the value of

x_R

(in cm) is ______.

Q173·PhysicsSingle correctJEE Main 2020

A particle moving in the xy plane experiences a velocity dependent force

\vec{F} = k\left(v_{y}\hat{i} + v_{x}\hat{j}\right)

, where

v_{x}

and

v_{y}

are the x and y components of its velocity

\vec{v}

. If

\vec{a}

is the acceleration of the particle, then which of the following statements is true for the particle?

(A)quantity $\vec{v} × \vec{a}$ is constant in time
(B) $\vec{F}$ arises due to a magnetic field.
(C)kinetic energy of particle is constant in time.
(D)quantity $\vec{v} · \vec{a}$ is constant in time.

Q174·PhysicsSingle correctJEE Main 2020

An insect is at the bottom of a hemispherical ditch or radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is:

\left(g=10\,ms^{-2}\right)

(A)0.20 m
(B)0.45 m
(C)0.60 m
(D)0.80 m

Q175·PhysicsSingle correctJEE Main 2020

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate

\dfrac{dM(t)}{dt} = bv^{2}(t)

, where v(t) its instantaneous velocity. The instantaneous acceleration of the satellite is:

(A) $-\dfrac{2bv^{3}}{M(t)}$
(B) $-\dfrac{bv^{3}}{M(t)}$
(C) $-bv(t)$
(D) $-\dfrac{bv^{3}}{2M(t)}$

Q176·PhysicsSingle correctJEE Main 2020

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv

^{2}

where v is it speed. The maximum height attained by the ball is:

(A) $\frac{1}{k}\ln\left(1+\frac{ku^{2}}{2g}\right)$
(B) $\frac{1}{2k}\tan^{-1}\frac{ku^{2}}{g}$
(C) $\frac{1}{k}\tan^{-1}\frac{ku^{2}}{2g}$
(D) $\frac{1}{2k}\ln\left(1+\frac{ku^{2}}{g}\right)$

Q177·PhysicsNumericalJEE Main 2020

A block starts moving up an inclined plane of inclination

30^{\circ}

with an initial velocity of

v_{0}

. It comes back to its initial position with velocity

\frac{v_{0}}{2}

. The value of the coefficient f kinetic friction between the block and the inclined plane is close to

\frac{I}{1000}

, The nearest integer to I is

Q178·PhysicsSingle correctJEE Main 2020

A spring mass system (mass m, spring constant k and natural length

\ell

) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity

\omega

,

(k >> m\omega^{2})

the relative change in the length of the spring is best given by the option:

(A) $\frac{m\omega^{2}}{3k}$
(B) $\frac{m\omega^{2}}{k}$
(C) $\frac{2m\omega^{2}}{3k}$
(D) $\sqrt{\frac{2}{3}}\left(\frac{m\omega^{2}}{k}\right)$

Q179·PhysicsSingle correctJEE Main 2020

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length

\ell

. The other end is fixed. The system is given an angular speed

\omega

about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

(A) $\dfrac{m\ell\omega^{2}}{k+m\omega}$
(B) $\dfrac{m\ell\omega^{2}}{k+m\omega^{2}}$
(C) $\dfrac{m\ell\omega^{2}}{k-\omega m}$
(D) $\dfrac{m\ell\omega^{2}}{k-m\omega^{2}}$

Q180·PhysicsSingle correctJEE Main 2020

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45° with the vertical. Then F equals: (Take g = 10 ms

^{-2}

and the rope to be massless)

(A)100 N
(B)75 N
(C)70 N
(D)90 N

Q181·PhysicsMultiple correctJEE Advanced 2019

A block of mass 2M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are

a_1

,

a_2

and

a_3

as shown in the figure. the system is released from rest with the spring in its unstretched state. The maximum extension of the spring is

x_0

. Which of the following option(s) is/are correct? [g is the acceleration due to gravity. neglect friction]

(A) $a_2 - a_1 = a_1 - a_3$
(B)At an extension of $\frac{x_0}{4}$ of the spring, the magnitude of acceleration of the block connected to the spring is $\frac{3g}{10}$
(C) $x_0 = \frac{4Mg}{k}$
(D)When spring achieves an extension of $\frac{x_0}{2}$ for the first time, the speed of the block connected to the spring is $3g\sqrt{\frac{M}{5k}}$ .

Q182·PhysicsSingle correctJEE Main 2019

A smooth wire of length

2\pi r

is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed w about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of

\omega^{2}

is equal to:

(A) $\dfrac{\sqrt{3}\,g}{2r}$
(B) $(g\sqrt{3})/r$
(C) $2g/r$
(D) $2g/(r\sqrt{3})$

Q183·PhysicsSingle correctJEE Main 2019

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30º with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is m = 0.2. The difference between the accelerations of the block, in case (B) and case (A) will be : (g = 10 ms

^{-2}

)

(A)0.4 ms $^{-2}$
(B)3.2 ms $^{-2}$
(C)0 ms $^{-2}$
(D)0.8 ms $^{-2}$

Q184·PhysicsSingle correctJEE Main 2019

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms

^{-1}

with respect to the man. The speed of the man with respect to the surface is :

(A)0.47 ms $^{-1}$
(B)0.28 ms $^{-1}$
(C)0.14 ms $^{-1}$
(D)0.20 ms $^{-1}$

Q185·PhysicsSingle correctJEE Main 2019

A ball is thrown upward with an initial velocity V

_{0}

from the surface of the earth. The motion of the ball is affected by a drag force equal to m

\gamma

v

^{2}

(where m is mass of the ball, v is its Instantneous velocity and

\gamma

is a constant). Time taken by the ball to rise to its zenith is:

(A) $\dfrac{1}{\sqrt{\gamma g}}\ln\left(1+\sqrt{\dfrac{\gamma}{g}}V_{0}\right)$
(B) $\dfrac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\dfrac{\gamma}{g}}V_{0}\right)$
(C) $\dfrac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\dfrac{\gamma}{g}}V_{0}\right)$
(D) $\dfrac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\dfrac{2\gamma}{g}}V_{0}\right)$

Q186·PhysicsSingle correctJEE Main 2019

Two blocks A and B of masses

m_{A}

= 1 kg and

m_{B}

= 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontal, so that the block A does not slide over the block B is: [Take g = 10 m/s

^{2}

]

(A)8 N
(B)16 N
(C)12 N
(D)40 N

Q187·PhysicsSingle correctJEE Main 2019

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : [Take g = 10 m/s

^{2}

]

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

Q188·PhysicsSingle correctJEE Main 2019

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is:

(A) $2\sqrt{\frac{k}{p}}$
(B) $2\sqrt{\frac{p}{k}}$
(C) $\sqrt{\frac{2k}{p}}$
(D) $\sqrt{\frac{2p}{k}}$

Q189·PhysicsSingle correctJEE Main 2019

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take

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

)

(A)32 N
(B)18 N
(C)23 N
(D)25 N

Q190·PhysicsSingle correctJEE Main 2019

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10

ms^{-2}

)

(A)200 N
(B)140 N
(C)70 N
(D)100 N

Q191·PhysicsSingle correctJEE Advanced 2016

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity

\omega

is an example of a non-inertial frame of reference. The relationship between the force

\vec{F}_{rot}

experienced by a particle of mass m moving on the rotating disc and the force

\vec{F}_{in}

experienced by the particle in an inertial frame of reference is

\vec{F}_{rot} = \vec{F}_{in} + 2m\left(\vec{v}_{rot} \times \vec{\omega}\right) + m\left(\vec{\omega} \times \vec{r}\right) \times \vec{\omega},

where

\vec{v}_{rot}

is the velocity of the particle in the rotating frame of reference and

\vec{r}

is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed

\omega

about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation axis

\left(\vec{\omega} = \omega\hat{k}\right)

. A small block of mass m is gently placed in the slot at

\vec{r} = (R/2)\hat{i}

at t = 0 and is constrained to move only along the slot. The net reaction of the disc on the block is

(A) $-m\omega^{2}R\cos \omega t\,\hat{j} - mg\hat{k}$
(B) $m\omega^{2}R\sin \omega t\,\hat{j} - mg\hat{k}$
(C) $\frac{1}{2}m\omega^{2}R\left(e^{\omega t} - e^{-\omega t}\right)\hat{j} + mg\hat{k}$
(D) $\frac{1}{2}m\omega^{2}R\left(e^{2\omega t} - e^{-2\omega t}\right)\hat{j} + mg\hat{k}$

Q192·PhysicsSingle correctJEE Advanced 2016

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity

\omega

is an example of a non-inertial frame of reference. The relationship between the force

\vec{F}_{rot}

experienced by a particle of mass m moving on the rotating disc and the force

\vec{F}_{in}

experienced by the particle in an inertial frame of reference is

\vec{F}_{rot} = \vec{F}_{in} + 2m\left(\vec{v}_{rot} \times \vec{\omega}\right) + m\left(\vec{\omega} \times \vec{r}\right) \times \vec{\omega},

where

\vec{v}_{rot}

is the velocity of the particle in the rotating frame of reference and

\vec{r}

is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed

\omega

about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation axis

\left(\vec{\omega} = \omega\hat{k}\right)

. A small block of mass m is gently placed in the slot at

\vec{r} = (R/2)\hat{i}

at t = 0 and is constrained to move only along the slot. The distance r of the block at time t is

(A) $\frac{R}{4}\left(e^{2\omega t} + e^{-2\omega t}\right)$
(B) $\frac{R}{2}\cos 2\omega t$
(C) $\frac{R}{2}\cos \omega t$
(D) $\frac{R}{4}\left(e^{\omega t} + e^{-\omega t}\right)$

Q193·PhysicsMultiple correctJEE Advanced 2014

In the figure, a ladder of mass

m

is shown leaning against a wall. It is in static equilibrium making an angle

\theta

with the horizontal floor. The coefficient of friction between the wall and the ladder is

\mu_1

and that between the floor and the ladder is

\mu_2

. The normal reaction of the wall on the ladder is

N_1

and that of the floor is

N_2

. If the ladder is about to slip, then

(A) $\mu_1 = 0 \; \mu_2 \neq 0$ and $N_2 \tan \theta = \frac{mg}{2}$
(B) $\mu_1 \neq 0 \; \mu_2 = 0$ and $N_1 \tan \theta = \frac{mg}{2}$
(C) $\mu_1 \neq 0 \; \mu_2 \neq 0$ and $N_2 = \frac{mg}{1+\mu_1\mu_2}$
(D) $\mu_1 = 0 \; \mu_2 \neq 0$ and $N_1 \tan \theta = \frac{mg}{2}$

Q194·PhysicsSingle correctJEE Advanced 2014

A block of mass

m_{1} = 1

kg another mass

m_{2} = 2

kg, are placed together (see figure) on an inclined plane with angle of inclination

\theta

. Various values of

\theta

are given in List I. The coefficient of friction between the block

m_{1}

and the plane is always zero. The coefficient of static and dynamic friction between the block

m_{2}

and the plane are equal to

\mu = 0.3

. In List II expressions for the friction on the block

m_{2}

are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by

g

. [Useful information:

\tan(5.5^{\circ}) \approx 0.1

;

\tan(11.5^{\circ}) \approx 0.2

;

\tan(16.5^{\circ}) \approx 0.3

]

List I	List II
P. $\theta = 5^{\circ}$	1. $m_{2}g\sin\theta$
Q. $\theta = 10^{\circ}$	2. $(m_{1}+m_{2})g\sin\theta$
R. $\theta = 15^{\circ}$	3. $\mu m_{2}g\cos\theta$
S. $\theta = 20^{\circ}$	4. $\mu(m_{1}+m_{2})g\cos\theta$

(A)P-1, Q-1, R-1, S-3
(B)P-2, Q-2, R-2, S-3
(C)P-2, Q-2, R-2, S-4
(D)P-2, Q-2, R-3, S-3

Q195·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 magnitude of the normal reaction that acts on the block at the point Q is

(A) $7.5\ \mathrm{N}$
(B) $8.6\ \mathrm{N}$
(C) $11.5\ \mathrm{N}$
(D) $22.5\ \mathrm{N}$

Q196·PhysicsSingle correctJEE Advanced 2013

A particle of mass m is projected from the ground with an initial speed

u_{0}

at an angle

\alpha

with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed

u_{0}

. The angle that the composite system makes with the horizontal immediately after the collision is

(A) $\frac{\pi}{4}$
(B) $\frac{\pi}{4}+\alpha$
(C) $\frac{\pi}{4}-\alpha$
(D) $\frac{\pi}{2}$

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