Question

Two discs one of density $7.2g/c{m}^3$ and the other of density $8.9g/c{m}^3$, 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 $\frac{r_1^2}{r_2^2}=\frac{{\rho }_2}{{\rho }_1}$
$\therefore \frac{I_1}{I_2}=\frac{{\rho }_2}{{\rho }_1}=\frac{8.9}{7.2}$