Question

The radius of gyration of a regular solid cylinder of radius $R$ about its axis is

• A. $\frac{R}{2}$
• B. $R$
• C. $\frac{R}{\sqrt{2}}$
• D. $2R$
• E. $\frac{R}{4}$

Hint:

The radius of gyration is a measure of how mass is distributed around the axis of rotation.

Answer 1

The Correct Option is C

Step 1: The moment of inertia of a solid cylinder about its central axis is: \[ I = \frac{1}{2} M R^2 \] Step 2: The radius of gyration $K$ is related to the moment of inertia by: \[ I = M K^2 \] Step 3: Equating both expressions: \[ M K^2 = \frac{1}{2} M R^2 \] \[ K^2 = \frac{R^2}{2} \] \[ K = \frac{R}{\sqrt{2}} \] Step 4: Therefore, the correct answer is (C).