Question

Two discs one of density $7.2\, g / cm ^3$ and the other of density $8.9\, g / cm ^3$, are of same mass and thickness. Their moments of inertia are in the ratio

• A. $8.9: 7.2$
• B. $7.2: 8.9$
• C. $(8.9 \times 7.2): 1$
• D. $1:(8.9 \times 7.2)$

Answer 1

Answer: (A)

$\frac{I_1}{I_2}=\frac{\frac{1}{2} M_1 r_1^2}{\frac{1}{2} M_2 r_2^2}=\frac{r_1^2}{r_2^2}$
As masses of two discs are equal, hence
$\left(\pi r_1^2 t\right) \rho_1=\left(\pi r_2^2 t\right) \rho_2$
or $ \frac{r_1^2}{r_2^2}=\frac{\rho_2}{\rho_1}$
$\therefore \frac{I_1}{I_2}=\frac{\rho_2}{\rho_1}=\frac{8.9}{7.2}$