NEET (UG) 2023 — Question 1

Moment of inertia of solid sphere: $I_1 = \frac{2}{5}MR^2$. Moment of inertia of thin hollow sphere: $I_2 = \frac{2}{3}MR^2$. Radius of gyration: $k = \sqrt{I/M}$. Thus $k_1 = \sqrt{\frac{2}{5}}R$, $k_2 = \sqrt{\frac{2}{3}}R$. Ratio $\frac{k_1}{k_2} = \frac{\sqrt{2/5}}{\sqrt{2/3}} = \sqrt{\frac{3}{5}} = \frac{\sqrt{3}}{\sqrt{5}}$. Hence the ratio is $\sqrt{3}:\sqrt{5}$ which corresponds to option D.