Uniform Circular Motion – Acceleration – Rankers Physics
Topic: Circular Motion
Subtopic: Non Uniform Circular Motion

Uniform Circular Motion – Acceleration


Assertion (A): A particle moving at constant speed and constant magnitude of radial acceleration must be undergoing uniform circular motion.
Reason (R): In uniform circular motion speed cannot change as there is no tangential acceleration.
 
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

Assertion (A): Constant speed and constant magnitude of radial acceleration ((v^2/r)) imply constant radius ((r)), which defines uniform circular motion. So (A) is True.
Reason (R): In uniform circular motion, acceleration is purely centripetal (radial), with no component tangential to the path. Thus, speed remains constant. So (R) is True.
Reason (R) correctly explains why constant speed and constant radial acceleration magnitude lead to uniform circular motion by implying constant radius and absence of tangential acceleration.

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