Question

The radius of gyration K of a hollow sphere of mass M and radius R about an axis XY is equal to R as shown in figure. The distance of that axis from the center of the sphere is h. The value of h is

• A. \(\frac{R}{\sqrt{3}}\)
• B. \(\frac{R}{2}\)
• C. \(\frac{R}{\sqrt{2}}\)
• D. \(\frac{2R}{\sqrt{3}}\)

Hint:

Use the parallel axis theorem on the moment of inertia of a thin hollow sphere.

Answer 1

The Correct Option is A

Step 1: Write $K$ in two ways:
About the centre: $K_{cm}^2 = \frac23 R^2$. About a parallel axis: $K^2 = K_{cm}^2 + h^2$.

Step 2: Solve for $h$:
$h^2 = R^2 - \frac23 R^2 = \frac13 R^2$, so $h = \frac{R}{\sqrt3}$.

Final Answer:
$h = \frac{R}{\sqrt{3}}$, option (A). \[ \boxed{\frac{R}{\sqrt{3}}} \]