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. $\frac{8.9}{7.2}$
• B. $\frac{7.2}{8.9}$
• C. $(8.9\times 7.2):1$
• D. $1:(8.9\times 7.2)$

Answer 1

The correct option is A $\frac{8.9}{7.2}$

Let $R_1,{\rho }_1,t$ and $R_2,{\rho }_2,t$ be the radius and density and thickness of discs respectively.

$M_1={\rho }_1\pi R_1^{2}t$ and $M_2={\rho }_2\pi R_2^{2}t$

But $M_1=M_2⟹\frac{R_1^2}{R_2^2}=\frac{{\rho }_2}{{\rho }_1}$

Now, $I=\frac{1}{2}M{R}^2$

Thus, $\frac{I_1}{I_2}=\frac{R_1^2}{R_2^2}=\frac{{\rho }_2}{{\rho }_1}=\frac{8.9}{7.2}$