Question

Two spheres of equal masses, one of which is a thin spherical shell and the other a solid, have the same moment of inertia about their respective diameters. The ratio of their radii will be.

• A. $5:7$
• B. $3:5$
• C. $\sqrt{3}:\sqrt{5}$
• D. $\sqrt{3}:\sqrt{7}$

Answer 1

The correct option is C $\sqrt{3}:\sqrt{5}$

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