Question

The ratio of radii of two solid spheres of same material is $1:2$. The ratio of moments of inertia of smaller and larger spheres about axes passing through their centres is:

• A. $1:4$
• B. $1:8$
• C. $1:16$
• D. $1:32$

Answer 1

The correct option is D $1:32$

Let the density of sphere be $\rho$

Now for the bigger sphere let the radius be 2R,

$M_1=\frac{4\pi (2R{)}^3}{3}$

Now for smaller sphere let the radius be R , $M_2=\frac{4\pi (R{)}^3}{3}$,

So $M_1=8M_2$

Moment of inertia of bigger sphere $I_1=\frac{2M_1(2R{)}^2}{5}$

Moment of inertia of smaller sphere $I_2=\frac{2M_2(R{)}^2}{5}$

So $\frac{I_2}{I_1}=1:32$