Question

Two solid sphere are made of the same material. The ratio of their diameters is $2:1$. The ratio of their moment of inertia about their respective diameters is:

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

Answer 1

The correct option is D $16:1$

$I=\frac{2}{5}m{r}^2=\frac{2}{5}\rho 4\pi r^4$

$\frac{I_1}{I_2}=\frac{r_1^4}{r_2^4}=\frac{d_1^4}{d_2^4}=\frac{2^4}{1^4}=\frac{16}{1}$