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.
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
View Answer
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.
Assertion (A): Moment of inertia about an axis passing through center of mass is maximum.
Reason (R): Theorem of parallel axis can be applied only for two dimensional body of negligible thickness.
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
View Answer
Assertion (A) is false because the moment of inertia about an axis passing through the center of mass is the minimum, not maximum, for parallel axes (\(I = I_{CM} + Md^2\)).
Reason (R) is false because the parallel axis theorem is applicable to any rigid body, not just 2D bodies of negligible thickness.