Engineering
Physics
Acceleration
Center of Mass
Angular Momentum and Conservation of Angular Momentum
Question

Match the column

Column-I Column-II
(A) Velocity of its centre of mass changes (P) A stone is tied to one end of a string and is revolving with constant angular velocity in a horizontal circle having centre O.
(B) Its angular momentum about point O is constant (Q) A block is projected on rough level ground from point O.
(C) Its kinetic energy is constant (R) A ball is dropped from a plane flying horizontally with constant velocity. Neglect air resistance. Point O is point of projection on plane from which the ball is dropped.
  (S) A uniform sphere is in pure rolling, rolling down an inclined plane where O is the centre of the sphere.
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Solution
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This question tests understanding of conservation laws and motion types. For each scenario (P, Q, R, S), analyze if the velocity of the center of mass changes (A), if angular momentum about point O is constant (B), or if kinetic energy is constant (C).

For example, in (P): A stone in uniform circular motion has constant speed, so its kinetic energy (12mv2) is constant (C). Its velocity direction changes, so center of mass velocity changes (A). Angular momentum about O is constant as force is central.

Final Answer: (A) matches (P), (R); (B) matches (P), (S); (C) matches (P), (S).