Question

A solid sphere of radius R has moment of inertia \(I\) about its diameter. What will be moment of inertia of a shell of same mass and same radius about its diameter?

• A. \( \frac{3}{5}I \)
• B. \( \frac{5}{3}I \)
• C. \( \frac{2}{3}I \)
• D. \( \frac{2}{5}I \)

Hint:

Remember standard results: solid sphere \( \frac{2}{5}MR^2 \), shell \( \frac{2}{3}MR^2 \).

Answer 1

The Correct Option is B

Concept: Moment of inertia: \[ I_{\text{solid sphere}} = \frac{2}{5}MR^2 \] \[ I_{\text{shell}} = \frac{2}{3}MR^2 \]

Step 1: Given relation.
\[ I = \frac{2}{5}MR^2 \Rightarrow MR^2 = \frac{5}{2}I \]

Step 2: Shell moment of inertia.
\[ I_{\text{shell}} = \frac{2}{3}MR^2 = \frac{2}{3} \cdot \frac{5}{2}I = \frac{5}{3}I \]