When the road is dry and coefficient of friction is $\mu $, the maximum speed of a car in a circular path is 10 ${\rm{m}}{{\rm{s}}^{ - 1}}$. If the road becomes wet and $\mu ' = \mu /2$, what is the maximum speed permitted?

$5\sqrt 2 {\rm{\;m}}{{\rm{s}}^{ - 1}}$

$5\,{\rm{\;m}}{{\rm{s}}^{ - 1}}$

$10\,{\rm{\;m}}{{\rm{s}}^{ - 1}}$

$10\sqrt 2 {\rm{\;m}}{{\rm{s}}^{ - 1}}$

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JEE • PHYSICS • LAWS OF MOTION

Laws of motion practice · Medium

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1 Medium

1 of 384

Application +4 | -1

A machine gun has a mass

5 {~kg}

. It fires 50 gram bullets at the rate of 30 bullets per minute at a speed of

400 {~ms}^{-1}

. What force is required to keep the gun in position?

View answer and explanation

Correct option: A

10 {~N}

Option A (

10 {~N}

) is correct because the force required to keep the gun in position is equal to the rate of change of momentum of the bullets fired.

2 Medium

2 of 384

Application +4 | -1

A particle of mass

4 {~m}

which is at rest explodes into three fragments. Two of the fragments each of mass

m

are found to move with a speed of

v

each in mutually perpendicular direction. The total energy released in the process is

View answer and explanation

Correct option: D

\frac{3}{2} m v^2

Option D (

\frac{3}{2} m v^2

) is correct because the total energy released is the sum of kinetic energies of all fragments, calculated using conservation of momentum.

3 Medium

3 of 384

Application +4 | -1

A block of mass ‘m’ rests on a rough inclined plane making an angle

30^\circ

with the horizontal. The co-efficient of static friction between the block and the plane is 0.8. If force of friction on the block is 10 N, the mass of the block is

\left( {g = 10\,m{s^{ - 2}}} \right).

View answer and explanation

Correct option: D

2 kg

Option D (2 kg) is correct because the mass is calculated using the equilibrium condition on the inclined plane where the force of friction equals the component of weight along the plane.

4 Medium

4 of 384

Analyzing +4 | -1

Statement-1: A shell at the origin explodes into three pieces of masses

1 \mathrm{~kg}, 2 \mathrm{~kg}

and

m \mathrm{~kg}

. The

1 \mathrm{~kg}

and

2 \mathrm{~kg}

pieces fly off with speeds

12 \mathrm{~m} / \mathrm{s}

along the

x

-axis and

8 \mathrm{~m} / \mathrm{s}

along the

y

-axis respectively. If

{m} \,\mathrm{kg}

piece flies off with speed

40 \mathrm{~m} / \mathrm{s}

, the total mass of the shell must be

3.5 \mathrm{~kg}

.
Statement-2: The law of conservation of linear momentum holds good.

View answer and explanation

Correct option: A

Statement-1 is true, Statement-2 is true, Statement-2 is the correct explanation for Statement-1

Option D is correct because the law of conservation of linear momentum is applied to find the mass of the third piece, making Statement-2 the correct explanation for Statement-1.

5 Medium

5 of 384

Understanding +4 | -1

For a system to follow the law of conservation of linear momentum during a collision , the condition is
Total external force acting on the system is zero.
Total external force acting on the system finite and time of collision is negligible.
Total internal force acting on the system is zero.

View answer and explanation

Correct option: A

(1)only

Option A ((1)only) is correct because the law of conservation of linear momentum holds when the total external force acting on the system is zero.

6 Medium

6 of 384

Application +4 | -1

If force on a rocket having exhaust velocity of

300 \mathrm{~m} / \mathrm{sec}

is 210 N, then rate of combustion of the fuel is:

View answer and explanation

Correct option: A

0.7 kg/s

Option A (0.7 kg/s) is correct because it is the rate of combustion calculated using the thrust force and exhaust velocity.

7 Medium

7 of 384

Understanding +4 | -1

Which one of following is a characteristic of force?

View answer and explanation

Correct option: B

Cannot make a moving object to increase speed.

Option A is correct because force can initiate movement in a stationary object, while options B, C, and D are incorrect as force can also increase/decrease speed and change direction.

8 Medium

8 of 384

Understanding +4 | -1

An object will continue moving uniformly when

View answer and explanation

Correct option: C

the resultant force on it is zero

Option C (the resultant force on it is zero) is correct because, according to Newton's First Law, an object continues moving uniformly (constant velocity) when no net force acts upon it.

9 Medium

9 of 384

Understanding +4 | -1

Assertion : On a rainy day, it is difficult to drive a car or bus at high speed.
Reason : The value of coefficient of friction is lowered due
to wetting of the surface.

View answer and explanation

Correct option: A

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Option A is correct because the assertion and reason are both true, and the reason correctly explains why driving at high speed is difficult on a rainy day due to the reduced coefficient of friction.

10 Medium

10 of 384

Analyzing +4 | -1

A solid cylinder and a hollow cylinder are released from the same point an inclined plane of inclination

\theta

. If the coefficient of static friction is not sufficient to prevent slipping then at the bottom of the incline plane.

View answer and explanation

Correct option: C

Both will have same linear velocity

The correct answer is Both will have same linear velocity because the acceleration of the center of mass does not depend on the shape, size, or mass of the body when slipping occurs.

11 Medium

11 of 384

Application +4 | -1

Same force acts on two bodies of different masses 3 kg and 5 kg initially at rest. The ratio of times required to acquire same final velocity is

View answer and explanation

Correct option: D

0.128472222

Option D (03:05) is correct because the ratio of times is inversely proportional to the ratio of accelerations, which is directly proportional to the ratio of masses.

12 Medium

12 of 384

Understanding +4 | -1

In order to prevent slipping while walking on ice, one should take smaller steps because of the

View answer and explanation

Correct option: C

smaller friction

Option C (smaller friction) is correct because smaller steps reduce the force needed, minimizing the risk of exceeding the available static friction on ice.

13 Medium

13 of 384

Understanding +4 | -1

A body is imparted motion from rest to move in a straight line. If it is then obstructed by an opposite force, then

View answer and explanation

Correct option: B

The body is sure to slow down

Option B is correct because an opposing force will cause the body to decelerate, thus slowing down.

14 Medium

14 of 384

Application +4 | -1

A 120 kg dolphin decelerates from 15 m/s to 7.5 m/s in 5 s to join another dolphin in play. What average force was exerted to slow the first dolphin if it was moving horizontally? (Assume that gravitational force is balanced by the buoyant force of the water)

View answer and explanation

Correct option: C

180 N

Option C (180 N) is correct because it is calculated using Newton's second law,

F = ma

, where 'a' is the deceleration of the dolphin.

15 Medium

15 of 384

Understanding +4 | -1

If a shell fired from a cannon ,explodes in mid air, then

View answer and explanation

Correct option: A

Its total kinetic energy increases

The correct answer is A (Its total kinetic energy increases) because the explosion converts chemical energy into kinetic energy of the fragments.

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16 Medium

16 of 384

Application +4 | -1

A balloon of mass

M

is descending at a constant acceleration

\alpha

. When a mass

m

is released from the balloon, it starts rising with the same acceleration

\alpha

. Assuming that its volume does not change, what is the value of

m

View answer and explanation

Correct option: B

\frac{2 \alpha}{\alpha+g} M

Option B (

\frac{{2 \alpha}}{{\alpha+g}} M

) is correct because it's derived from setting up and solving equations for the balloon's motion during descent and ascent.

17 Medium

17 of 384

Understanding +4 | -1

For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is

View answer and explanation

Correct option: B

A driver in a sport car moving with a constant high speed of

200\mathrm{km\;}{\mathrm{h}^{ - 1}}

on a straight rod

Option B (A driver in a sport car moving with a constant high speed of

200\mathrm{km\;}{\mathrm{h}^{ - 1}}

on a straight rod) is correct because it represents a non-accelerating frame of reference.

18 Medium

18 of 384

Analyzing +4 | -1

A sphere of mass

m

is rolling without sliding along positive

x

-axis on a rough horizontal surface of coefficient of friction

\mu

. It elastically collides with a wall and then returns. The correct statement of frictional force

(f)

acting on the sphere is

View answer and explanation

Correct option: B

{f}=0 {mg} \vec{i}

before collision and

{f}=+\mu{mg} \vec{i}

after collision

Option D (

{f}=0 {mg} \vec{{i}}

before collision and

{f}=+\mu{mg} \vec{{i}}

after collision) is correct because before the collision, the sphere is in pure rolling, so friction is zero. After the elastic collision, the sphere slips, and kinetic friction acts.

19 Medium

19 of 384

Understanding +4 | -1

A box is placed on an inclined plane and has to be pushed down. The angle of inclination is

View answer and explanation

Correct option: D

Less than angle of repose

Option D (Less than angle of repose) is correct because if the angle of inclination were equal to or greater than the angle of repose, the box would slide down on its own without needing to be pushed.

20 Medium

20 of 384

Understanding +4 | -1

Consider the following statements and select the incorrect statement(s).
I. To move a football at rest, some one must kick it.
II. To throw a stone upwards, one has to give it an upward push.
III. A breeze causes the branches of a tree to become stationary.
IV. A strong wind can move even heavy objects.

View answer and explanation

Correct option: B

Only III

Option B (Only III) is correct because a breeze causes branches to swing, not become stationary.

21 Medium

21 of 384

Understanding +4 | -1

Three weights

w,2w\;\mathrm{and\;}3w

are connected to identical spring suspended from a rigid horizontal rod. The assembly of the rod and weights fall freely. The positions of the weight from the rod are such that

View answer and explanation

Correct option: C

All will be at the same distance

Option C (All will be at the same distance) is correct because in free fall, the apparent weight of each object is zero, so the springs will not be stretched, and all weights will be at the same distance from the rod.

22 Medium

22 of 384

Application +4 | -1

A motor cycle and a car are moving on a horizontal road with the same velocity. If they are brought to rest by the application of brakes, which provided equal retardation, then

View answer and explanation

Correct option: C

Both will stop at the same distance

Option C (Both will stop at the same distance) is correct because the stopping distance depends on the initial velocity and retardation, and both are the same for the motorcycle and the car.

23 Medium

23 of 384

Understanding +4 | -1

In relativity which is constant between two frames of reference

View answer and explanation

Correct option: D

Velocity

The correct answer is the speed of light. The second postulate of special relativity states that the speed of light in a vacuum is constant for all observers.

24 Medium

24 of 384

Remembering +4 | -1

Newton’s first law of motion describes the following

View answer and explanation

Correct option: C

Inertia

Option C (Inertia) is correct because Newton's first law of motion, also known as the law of inertia, describes the tendency of an object to resist changes in its state of motion.

25 Medium

25 of 384

Application +4 | -1

A batsman hits a ball of mass

0.2 {~kg}

straight towards the bowler without changing its initial speed of

6 {~m} / {s}

. What is the impulse imparted to the ball?

View answer and explanation

Correct option: B

2.4 \,{Ns}

Option B (2.4 Ns) is correct because the impulse imparted to the ball is equal to the change in momentum of the ball.

26 Medium

26 of 384

Application +4 | -1

An engine of power

58.8 \mathrm{~kW}

pulls a train of mass

2 \times 10^5 \mathrm{~kg}

with a velocity of

36 \mathrm{~km} \mathrm{~h}^{-1}

. The coefficient of friction is

View answer and explanation

Correct option: C

0.003

Option D is correct because the radius of the nucleus is calculated using the formula R = R0 * A^(1/3).

27 Medium

27 of 384

Understanding +4 | -1

Statement-I: Aeroplanes always fly at low altitudes.
Statement-II: According to Newton's third law of motion, for every action there is an equal and opposite reaction.

View answer and explanation

Correct option: A

Statement-I is true and statement-II is true

Option C (Statement-I is false and statement-II is true) is correct because aeroplanes fly at high altitudes and Newton's third law is always true.

28 Medium

28 of 384

Analyzing +4 | -1

Statement I: A bullet is fired from a rifle. If the rifle recoils freely, the kinetic energy of the rifle is less than that of the bullet.
Statement II: In the case of a rifle-bullet system, the law of conservation of momentum is violated.

View answer and explanation

Correct option: C

Statement I is true, Statement II is false

Option C is correct. Statement I is true because the rifle's kinetic energy is less than the bullet's due to the rifle's larger mass. Statement II is false because momentum is conserved in the rifle-bullet system.

29 Medium

29 of 384

Application +4 | -1

When the road is dry and coefficient of friction is

\mu

, the maximum speed of a car in a circular path is 10

\mathrm{m}{\mathrm{s}^{ - 1}}

. If the road becomes wet and

\mu ' = \mu /2

, what is the maximum speed permitted?

View answer and explanation

Correct option: D

5\sqrt 2 \mathrm{\;m}{\mathrm{s}^{ - 1}}

Option D (

5\sqrt 2 \;\mathrm{m}{\mathrm{s}^{ - 1}}

) is correct because the maximum speed is proportional to the square root of the coefficient of friction.

30 Medium

30 of 384

Understanding +4 | -1

A body at rest explodes into two equal parts. Then,

View answer and explanation

Correct option: D

They move with same speed in opposite directions

Option D (They move with same speed in opposite directions) is correct because due to conservation of momentum, the two equal parts must move with equal speeds in opposite directions to maintain zero total momentum.

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Key Takeaways

✓ This set contains 384 single-correct-answer MCQs on LAWS OF MOTION.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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