Physics - Rotation Question with Solution | TestHub

Let the radii of the thin spherical shell and the solid sphere are $R_1$ and $R_2$ respectively. Then the moment of inertia of the spherical shell about their diameter $I=\frac{2}{3}M{R}_1^2$ ...(i) and the moment of inertia of the solid sphere is given by $I=\frac{2}{5}M{R}_2^2$ ...(ii) Given that the masses and moment of inertia for both the bodies are equal, then from Eqs. (i) and (ii) $$\begin{array}{r}\frac{2}{3}M{R}_1^2=\frac{2}{5}M{R}_2^2\Rightarrow \frac{R_1^2}{R_2^2}=\frac{3}{5}\\ \Rightarrow \frac{R_1}{R_2}=\sqrt{\frac{3}{5}}\Rightarrow R_1:R_2=\sqrt{3}:\sqrt{5}\end{array}$$