Physics - Rotation Question with Solution | TestHub

Let the mass of both spheres be $M$.

Let the radius of the thin spherical shell be $R_1$ and the radius of the solid sphere be $R_2$.

The moment of inertia of the thin spherical shell about its diameter is $I_1=\frac{2}{3}M{R}_1^2$.

The moment of inertia of the solid sphere about its diameter is $I_2=\frac{2}{5}M{R}_2^2$.

Given that $I_1=I_2$, we have:

$\frac{2}{3}M{R}_1^2=\frac{2}{5}M{R}_2^2$

$\frac{R_1^2}{R_2^2}=\frac{3}{5}$

$\frac{R_1}{R_2}=\frac{\sqrt{3}}{\sqrt{5}}$

The ratio of their radii is $\sqrt{3}:\sqrt{5}$.

Answer: $\sqrt{3}:\sqrt{5}$