Question

We have two spheres, one of which is hollow and the other is solid, have identical masses and moment of inertia about their respective diameters. The ratio of their radii is

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

Answer 1

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

Moment of Inertia of hollow sphere is $I_1=\frac{2}{3}m{r}_1^2$

Moment of Inertia of solid sphere is $I_2=\frac{2}{5}m{r}_2^2$

As moment of inertia is equal:

$I_1=I_2\frac{2}{3}m{r}_1^2=\frac{2}{5}m{r}_2^2\frac{r_1^2}{r_2^2}=\frac{3}{5}{r}_1:r_2=\sqrt{3}:\sqrt{5}$