Question

A solid sphere and a hollow sphere of the same mass have the same M.I. about their respective diameters the ratio of their radii will be.

Answer 1

We know moment of inertia of solid sphere $I_s=\frac{2}{5}{m}_s{R}_s^2$ and

moment of inertia of hollow sphere$I_H=\frac{2}{3}{m}_H{R}_H^2$As per question $I_s=I_H$

Now,

$\frac{2}{5}{m}_s{R}_s^2=\frac{2}{3}{m}_H{R}_H^2$

as the masses are equal the ratio of their radii will be

$\frac{R_s^2}{R_H^2}=\frac{\frac{2}{3}}{\frac{2}{5}}=\sqrt{\frac{5}{3}}$