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 sphers about axes passing through their centers is

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

Answer 1

Answer: (D)

Let the density of sphere be $\rho$
Now for the bigger sphere let the radius be $2R$,
$<br/>M_1=\frac{4\pi (2R{)}^3}{3}<br/>$
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 $\frac{I_2}{I_1}=1:32$