Radius of Gyration Dependence – Rankers Physics
Topic: Rotational Motion
Subtopic: Moment of Inertia

Radius of Gyration Dependence


Assertion (A): Value of radius of gyration of a body depends on axis of rotation.
Reason (R): Radius of gyration is rms distance of particles of the body from the axis of rotation.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Radius of gyration is defined as \( k = \sqrt{I/M} \), where \( I \) is the moment of inertia. Since \( I \) depends on the axis of rotation, \( k \) also depends on the axis of rotation. R correctly defines \( k \) as an RMS distance from the axis, which means its value depends on that axis. Both A and R are true, and R explains A.

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