A particle is projected up an inclined plane with initial speed $v = 20{\rm{m}}{{\rm{s}}^{ - 1}}$ at an angle ${\rm{\theta }} = 30^\circ $ with plane. The component of its velocity perpendicular to plane when it strikes the plane is

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

$10\sqrt 3 {\rm{\;m}}{{\rm{s}}^{ - 1}}$

$5\sqrt 3 {\rm{\;m}}{{\rm{s}}^{ - 1}}$

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NEET • PHYSICS • LAWS OF MOTION

Laws of motion practice · Medium

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1 Medium

1 of 161

Analyzing +4 | -1

(A): Two solid cylinders of different masses and radii take same time to roll down an inclined plane without slipping.
(R): Moment of inertia of two solid cylinders of different masses and radii about their natural axes are different.

View answer and explanation

Correct option: B

Both (A) and (R) are true and (R) is not the correct explanation of (A)

Option B (Both (A) and (R) are true and (R) is not the correct explanation of (A)) is correct because the time to roll down depends on the moment of inertia's *distribution*, not just its value, and both cylinders have different moments of inertia.

2 Medium

2 of 161

Analyzing +4 | -1

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:

View answer and explanation

Correct option: A

Statement I is true but Statement II is false

Option A (Statement I is true but Statement II is false) is correct because an elevator can move at uniform speed when weight equals tension, but the force on a person's feet is *less* than their weight when descending with increasing speed.

3 Medium

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Application +4 | -1

A particle is projected with a velocity

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

at an angle of

{60^0}

. At the highest point, it explodes into three particles of equal masses. One goes vertically upwards with a velocity

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

, the second particle goes vertically downwards. What is the velocity of third particle?

View answer and explanation

Correct option: C

300\,m{s^{ - 1}}

Option C (

300\\,m{s^{ - 1}}

) is correct because it is derived from applying the conservation of momentum at the highest point of the trajectory after the explosion.

4 Medium

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Understanding +4 | -1

Assertion : Mass is a measure of inertia of the body in linear motion.

Reason : Greater the mass, greater is the force required to change its state of rest or of uniform motion.

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 Assertion is correct, reason is correct; reason is a correct explanation for assertion. Mass is directly related to inertia, and greater mass implies greater resistance to change in motion.

5 Medium

5 of 161

Analyzing +4 | -1

An air tight cage in which a bird is sitting is suspended from a spring balance. If the bird starts flying, then the reading of the balance will

View answer and explanation

Correct option: C

Decreases

Option D is correct because when the bird flies, it exerts a downward force equal to its weight on the air, which then exerts an equal and opposite force on the cage, effectively keeping the reading unchanged.

6 Medium

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Application +4 | -1

A stone is dropped from a height h. It hits the ground with a certain momentum p. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

View answer and explanation

Correct option: B

0.41

Option B (0.41) is correct because the momentum is proportional to the square root of the height, and a 100% increase in height results in a

\sqrt{2}

increase in momentum, which is approximately a 0.41 change.

7 Medium

7 of 161

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 is correct because an inertial frame is one that is not accelerating. A car moving at a constant high speed on a straight road approximates an inertial frame.

8 Medium

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Analyzing +4 | -1

Which of the following sets of forces can not have resultant force equal to zero. (All forces are in newton).

View answer and explanation

Correct option: D

10, 20, 40

Option D (10, 20, 40) is correct because the sum of the two smallest forces (10 + 20 = 30) is less than the largest force (40), so they cannot balance each other.

9 Medium

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Remembering +4 | -1

Newton’s Second law gives the measure of

View answer and explanation

Correct option: B

Force

Option B (Force) is correct. Newton's Second Law states that force is proportional to the rate of change of momentum, or F=ma.

10 Medium

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Understanding +4 | -1

A student unable to answer a question on Newton’s law of motion attempts to pull himself up by tugging on his hair. He will not succeed

View answer and explanation

Correct option: D

As the force applied is internal to the system

Option D is correct because pulling oneself up by tugging on one's hair is an internal force within the system (student), and internal forces cannot cause a change in the system's center of mass motion.

11 Medium

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Analyzing +4 | -1

A block of mass

\mathrm{m}

is kept on a moving block of mass

\mathrm{M}

in such a way that

\mathrm{M}

moves but

\mathrm{m}

remains at rest with respect to

\mathrm{M}

. Then

View answer and explanation

Correct option: C

Kinetic energy and momentum may be zero in a frame

Option C (Kinetic energy and momentum may be zero in a frame) is correct because if the frame of reference is moving with the block M, then the block m will be at rest in that frame, resulting in zero kinetic energy and momentum.

12 Medium

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Analyzing +4 | -1

STATEMENT-1 : A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

STATEMENT-2 : For every action there is an equal and opposite reaction.

View answer and explanation

Correct option: B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Option B (Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1) is correct because the cloth can be pulled out due to inertia, and Newton's third law is a separate concept.

13 Medium

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Application +4 | -1

A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then maximum velocity with which the car can move is

View answer and explanation

Correct option: B

14 m/s

The maximum velocity is calculated by equating the centripetal force with the maximum frictional force and solving for velocity. Therefore, the correct answer is B (14 m/s).

14 Medium

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Analyzing +4 | -1

Which of the following statement (s) is/are correct?

I. A string has a mass

m

. If it is accelerated, tension is non-uniform and if it is not accelerated, tension is uniform.

II. Tension force is an electromagnetic force.

View answer and explanation

Correct option: B

Only II

Option B (Only II) is correct because tension is indeed an electromagnetic force, while a string under acceleration will have non-uniform tension due to its mass.

15 Medium

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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 acceleration is the same for all weights, so the springs will be unstretched.

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16 Medium

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Analyzing +4 | -1

Choose the incorrect statement(s) from the following.
I. If a body is not in rest position, then the net external force acting on it cannot be zero.
II. If the net force acting on a body be zero then the body
will essentially remain at rest.

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because both statements are incorrect. A body can move with constant velocity if the net external force is zero, and a body will remain at rest or in uniform motion if the net force is zero.

17 Medium

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Understanding +4 | -1

A cyclist bends while taking turn in order to

View answer and explanation

Correct option: B

provide required centripetal force

Option B (provide required centripetal force) is correct because bending allows the cyclist to lean into the turn, providing a component of the normal force that acts as the centripetal force required for circular motion.

18 Medium

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Remembering +4 | -1

Newton’s first law of motion describes the following

View answer and explanation

Correct option: C

Inertia

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

19 Medium

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Analyzing +4 | -1

Assertion (A) : Two frames

S_1

and

S_2

are non-inertial. Then frame

S_2

when observed from

S_1

is inertial.

Reason (R): A frame in motion is not necessarily a non-inertial frame.

View answer and explanation

Correct option: D

If Assertion is false but the Reason is true.

Option D (If Assertion is false but the Reason is true) is correct because non-inertial frames observed from each other are also non-inertial, and a frame in motion can be inertial if it moves with constant velocity.

20 Medium

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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 (The body is sure to slow down) is correct because an opposite force will cause a deceleration, reducing the body's speed.

21 Medium

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Application +4 | -1

A block of mass 2kg is kept on the floor of freely falling lift. During the free fall of the lift, the block is pulled horizontal with a force of 4N, the frictional force acting on the block is

{\mu _s} = 0.1

View answer and explanation

Correct option: D

zero

Option D (zero) is correct because in a freely falling lift, the effective weight of the block is zero, hence the normal force and consequently the friction force are also zero.

22 Medium

22 of 161

Application +4 | -1

A 30 kg block rests on a rough horizontal surface. A force of 200 N is applied on the block. The block acquires a speed of 4 m/s, starting from rest in 2 s. What is the value of coefficient of friction?

View answer and explanation

Correct option: C

0.47

Option C (0.47) is correct because it is calculated using Newton's second law and the definition of kinetic friction, considering the applied force and the resulting acceleration.

23 Medium

23 of 161

Understanding +4 | -1

In the above Question, if the string C is stretched slowly, then

View answer and explanation

Correct option: A

The portion AB of the string will break

Option A (The portion AB of the string will break) is correct. When C is stretched slowly, the tension in AB will be higher due to the weight.

24 Medium

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Understanding +4 | -1

Statement-I: Coefficient of friction can be greater than unity.
Statement-II: Force of friction is dependent on normal reaction and ratio of friction and normal reaction cannot exceed unity.

View answer and explanation

Correct option: B

Statement-I is true and statement-II is false

Statement-I is true, and Statement-II is false. The coefficient of friction can be greater than unity, and the force of friction's dependence on the normal reaction doesn't limit their ratio to below unity.

25 Medium

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Understanding +4 | -1

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

View answer and explanation

Correct option: A

Momentum

Option A (Momentum) is correct because at the maximum height, the object's velocity is momentarily zero, and momentum is the product of mass and velocity.

26 Medium

26 of 161

Application +4 | -1

A particle is projected up an inclined plane with initial speed

v = 20\mathrm{m}{\mathrm{s}^{ - 1}}

at an angle

\mathrm{\theta } = 30^\circ

with plane. The component of its velocity perpendicular to plane when it strikes the plane is

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because the component of velocity perpendicular to the plane remains constant in magnitude throughout the projectile motion.

27 Medium

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Application +4 | -1

A frictionless inclined plane of length l having inclination θ is placed inside a lift which is accelerating downward with an acceleration a(

<g

) . If a block is allowed to move, down the inclined plane, from rest, then the time taken by the block to slide from top of the inclined plane to the bottom of the inclined plane is

View answer and explanation

Correct option: D

\sqrt {\frac{{2l}}{{\left( {\mathrm{g} - a} \right)\sin \mathrm{\theta }}}}

Option D (

\sqrt {\frac{{2l}}{{\left( {\mathrm{g} - a} \right)\sin \mathrm{\theta }}}}

) is correct because the effective acceleration is reduced due to the downward acceleration of the lift.

28 Medium

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Analyzing +4 | -1

Consider a small block placed with zero velocity on a rough convey or belt moving with constant velocity. The block eventually comes to rest with respect to belt.
Statement-1: Net work done by kinetic friction on belt is zero.
Statement-2: The kinetic energy of the belt does not change.

View answer and explanation

Correct option: D

Statement- 1 is false, Statement-2 is true

Option D is correct because the net work done by kinetic friction on the belt is negative, not zero, and the kinetic energy of the belt remains constant.

29 Medium

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Analyzing +4 | -1

A weight '

m g

' is suspended from the middle of a rope whose ends are rigidly clamped at the same level. The rope is no longer horizontal. What is the minimum tension required to completely straighten the rope?

View answer and explanation

Correct option: D

infinity

Option D (infinity) is correct. To completely straighten the rope, the tension must approach infinity to counteract the weight component acting downwards.

30 Medium

30 of 161

Understanding +4 | -1

An object is subjected to a force in the north-east direction. To balance this force, a second force should be applied in the direction

View answer and explanation

Correct option: C

South-west

Option C is correct because to balance a force, an equal and opposite force must be applied. The opposite of north-east is south-west.

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Key Takeaways

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