Question

Two uniform circular discs of same material, same thickness and at the same temperature have radii in the ratio $2:3$. The ratio of their momenta of inertia about the central axis is:

• A. $4:9$
• B. $16:81$
• C. $32:243$
• D. $8:27$

Answer 1

The correct option is B $16:81$

$I=\frac{M{r}^2}{2}$

$M=volume\times density=\pi r^2\times \rho$

$\frac{I_1}{I_2}=\frac{r_1^4}{r_2^4}=\frac{2^4}{3^4}=\frac{16}{81}$