Physics - Rotation Question with Solution | TestHub

Radius of gyration of solid sphere about its own axis is given by,

$k_{solid}=\sqrt{\frac{I}{M}}=\sqrt{\frac{{\displaystyle \frac{2M{R}^2}{5}}}{M}}=\sqrt{\frac{2}{5}}R$

Similarly,

$k_{hollow}=\sqrt{\frac{I}{M}}=\sqrt{\frac{{\displaystyle \frac{2M{R}^2}{3}}}{M}}=\sqrt{\frac{2}{3}}R$

Therefore, required ratio would be

$\frac{k_{solid}}{k_{hollow}}=\sqrt{\frac{3}{5}}$.

Note: This option was not present in the original paper.