JEE Advanced (Assertion-Reason Type): Rotational Motion | Chapter-wise Tests for JEE Main & Advanced PDF Download

Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has alternative choices, only one of which is the correct answer.
Q.1. Assertion : The centre of mass of a body may lie where there is no mass.
Reason : Centre of mass of body is a point, where the whole mass of the body is supposed to be concentrated.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (a)
As the concept of centre of mass is only theoretical, therefore in practice no mass may lie at the centre of mass. For example, centre of mass of a uniform circular ring is at the centre of the ring where there is no mass.

Q.2. Assertion : The earth is slowing down and as a result the moon is coming nearer to it.
Reason : The angular momentum of the earth moon system is conserved.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (d)
The earth is not slowing down. The angular momentum of the earth – moon system is conserved.

Q.3. Assertion : The position of centre of mass of body depend upon shape and size of the body.
Reason : Centre of mass of a body lies always at the centre of the body
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (c)
The position of centre of mass of a body depends on shape, size and distribution of mass of the body. The centre of mass does not lie necessarily at the centre of the body.

Q.4. Assertion : It is harder to open and shut the door if we apply force near the hinge.
Reason : Torque is maximum at hinge of the door.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (c)
Torque = Force × perpendicular distance of line of action of force from the axis of rotation (d).

Hence for a given applied force, torque or true tendency of rotation will be high for large value of d. If distance d is smaller, then greater force is required to cause the same torque, hence it is harder to open or shut down the door by applying a force near the hinge.

Q.5. Assertion: When axis of rotation passes through the centre of gravity, then the moment of inertia of a rigid body increases.
Reason: At the centre of gravity mass gets concentrated and moment of inertia increases.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (d)
The moment of inertia of a rigid body reduces to its minimum value, when the axis of rotation passes through its centre of gravity because the weight of a rigid body always acts through its centre of gravity.

Q.6. Assertion: An ice-skater stretches out arms-legs during performance.
Reason: Stretching out arms-legs helps the performer to balance his or her body so that he or she does not fall.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (c)
An ice-skater stretches out arms and legs during performance to take advantage of principle of conservation of angular momentum. As on doing so, their moment of inertia increases or decreases respectively and hence the angular velocity of spin motion decreases or increases accordingly.

Q.7. Assertion : If polar ice melts, days will be longer.
Reason : Moment of inertia decreases and thus angular velocity increases.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (c)
As the polar ice melts, water so formed flows towards the equator. The moment of inertia of the earth increases. To conserve angular momentum, angular velocity decreases. This increases the length (T = 2π/ω) of the day.

Q.8. Assertion : Moment of inertia of a particle is same, whatever be the axis of rotation
Reason : Moment of inertia depends on mass and distance of the particles.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (d)
The moment of inertia of a particle about an axis of rotation is given by the product of the mass of the particle and the square of the perpendicular distance of the particle from the axis of rotation. For different axis, distance would be different, therefore moment of inertia of a particle changes with the change in axis of rotation.

Q.9. Assertion: A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero.
Reason : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (d)
For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity, the acceleration of lowest point of disc is directed vertically upwards and is not zero (Due to translation part of rolling, acceleration of lowest point is zero. Due to rotational part of rolling, the tangential acceleration of lowest point is zero and centripetal acceleration is non-zero and upwards). Hence assertion is false.

Q.10. Assertion : The velocity of a body at the bottom of an inclined plane of given height, is more when it slides down the plane, compared to when it is rolling down the same plane.
Reason : In rolling, down, a body acquires both, kinetic energy of translation and rotation.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (a)
In sliding down, the entire potential energy is converted into kinetic energy. While in rolling down some part of potential energy is converted into K.E. of rotation. Therefore linear velocity acquired is less.