Question

A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is:

• A. 3 : 5
• B. 4 : 5
• C. 3 : 1
• D. 2 : 1

Hint:

Use the known formulas for the moment of inertia of a sphere and cylinder to find their ratio.

Answer 1

The Correct Option is A

The moment of inertia for a solid sphere about its diameter is: \[ I_{\text{sphere}} = \frac{2}{5} m r^2. \] The moment of inertia for a solid cylinder about its axis is: \[ I_{\text{cylinder}} = \frac{1}{2} m r^2. \] The ratio of the moment of inertia of the sphere to the cylinder is: \[ \frac{I_{\text{sphere}}}{I_{\text{cylinder}}} = \frac{\frac{2}{5} m r^2}{\frac{1}{2} m r^2} = \frac{4}{5}. \]