Radius of Gyration Dependence – Rankers Physics

Moment of Inertia: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Moment of Inertia. Understanding the underlying formula is key to arriving at the correct answer below:

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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