Rotational Motion– NDA Physics PYQs

NDA 2019-II

Q. 1. A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true?

(a)  The ring has higher kinetic energy

(b)  The disc has higher kinetic energy

(c)  The ring and the disc have the same kinetic energy

(d)  Kinetic energies of both the bodies are zero since they are not in linear motion

Answer: (a) The ring has higher kinetic energy

Explanation: Rotational KE = ½Iω². Ring: I_ring = MR². Disc: I_disc = ½MR². At the same ω: KE_ring = ½(MR²)ω² = ½MR²ω². KE_disc = ½(½MR²)ω² = ¼MR²ω². Since KE_ring > KE_disc, the ring has higher kinetic energy. Option (d) is wrong: rotating bodies have rotational kinetic energy even without linear motion. Concept Tested: Rotational kinetic energy: KE = ½Iω²; ring (I = MR²) > disc (I = ½MR²)

★ JOVIK Exam Insight Moment of inertia of ring vs disc: I_ring = MR², I_disc = ½MR². The ring concentrates all mass at radius R; the disc spreads mass from 0 to R. Higher I at same ω → higher rotational KE. NDA 2019-II tested both I comparison and KE comparison in the same paper.

Q. 2. A solid disc and a solid sphere have the same mass and same radius. Which one has the higher moment of inertia about its centre of mass?

(a)  The disc

(b)  The sphere

(c)  Both have the same moment of inertia

(d)  The information provided is not sufficient to answer the question

Answer: (a) The disc

Explanation: I_disc (solid, central axis) = ½MR² = 0.5MR². I_sphere (solid, about diameter) = (2/5)MR² = 0.4MR². Since 0.5 > 0.4, the solid disc has a higher moment of inertia. The disc concentrates more mass farther from the axis (at the rim) compared to the sphere, which distributes more mass near the centre. Concept Tested: Moment of inertia: solid disc (½MR² = 0.5MR²) > solid sphere (2/5 MR² = 0.4MR²)

NDA 2017-II

Q. 3. An object moves in a circular path with a constant speed. Which one of the following statements is correct?

(a)  The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).

(b)  The centripetal acceleration is greater for a gentle curve than that for a sharp curve.

(c)  The centripetal acceleration is the same for both, the gentle and sharp curves.

(d)  The centripetal acceleration causes the object to slow down.

Answer: (a) The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).

Explanation: Centripetal acceleration a_c = v²/r. At constant speed v, a_c is inversely proportional to radius r. A gentle curve has larger radius r, so smaller a_c. A sharp curve has smaller radius, so larger a_c. Centripetal acceleration does not slow down an object: it only changes direction. Slowing down requires a tangential (braking) force. Concept Tested: Centripetal acceleration: a_c = v²/r; larger radius → smaller centripetal acceleration

NDA 2013-I

Q. 4. If an object undergoes a uniform circular motion, then its

(a)  acceleration remains uniform

(b)  velocity changes

(c)  speed changes

(d)  velocity remains uniform

Answer: (b) velocity changes

Explanation: In uniform circular motion, speed is constant: but velocity is a vector (magnitude + direction). The direction of the velocity vector changes continuously as the object moves around the circle. Since velocity changes, acceleration is present (centripetal). Speed does not change. Acceleration direction changes continuously, so acceleration is not uniform. Concept Tested: Uniform circular motion: velocity (vector) changes continuously; speed is constant

★ JOVIK Exam Insight NDA has tested the speed-vs-velocity distinction in circular motion across 2013-I and 2017-II. Speed = constant. Velocity = changing (direction). Acceleration = changing (centripetal, always toward centre). These three facts together define uniform circular motion.

Q. 5. A car is moving with a uniform speed. However its momentum is changing. Then the car

(a)  may be on an elliptical path

(b)  is moving on a straight path without acceleration

(c)  is moving on a straight path with acceleration

(d)  is moving without any acceleration

Answer: (a) may be on an elliptical path

Explanation: Momentum p = mv is a vector. Uniform speed means constant |v|, but if direction changes, the velocity vector changes: and therefore momentum changes. This happens on any curved path: circular, elliptical, or any non-straight trajectory. On a straight path with constant speed, both speed and direction are constant, so momentum is constant. Changing momentum with constant speed implies a curved path. Concept Tested: Vector nature of momentum: constant speed + changing direction = changing momentum (curved path)

NDA 2010-II

Q. 6. A man is sitting on a rotating stool with his arms outstretched. If suddenly he folds his arm the angular velocity of the man would?

(a)  increase

(b)  decrease

(c)  become zero

(d)  remain constant

Answer: (a) increase

Explanation: By conservation of angular momentum: L = Iω = constant (no external torque acts). When the man folds his arms, mass is redistributed closer to the rotation axis: the moment of inertia I decreases. Since L = Iω is constant and I decreases, ω must increase. The man spins faster. Concept Tested: Conservation of angular momentum: decreasing I increases ω

★ JOVIK Exam Insight A classic NDA trap: students predict the angular velocity decreases (‘less effort = less spinning’). Wrong. No external torque → angular momentum is conserved. Smaller I → larger ω. Same principle as an ice skater pulling in arms to spin faster.

Q. 7. For a particle revolving in a circular path, the acceleration of the particle is?

(a)  along the tangent

(b)  along the radius

(c)  zero

(d)  along the circumference of the circle

Answer: (b) along the radius

Explanation: A particle in circular motion has centripetal acceleration directed toward the centre of the circle: along the radius (inward). Tangential direction would change speed, not direction. Acceleration along the circumference has no physical meaning. Zero acceleration would imply straight-line motion: not circular. Concept Tested: Centripetal acceleration: directed along the radius toward the centre of the circle

★ JOVIK Exam Insight The most common wrong answer is (c) zero: because ‘the speed is constant.’ This is wrong. Acceleration = rate of change of VELOCITY (a vector), not speed. Velocity direction changes continuously in circular motion → acceleration exists and is centripetal.

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