Q. Two discs have same mass and thickness. Their materials are of densities $\rho_{1}$ and $\rho_{2}$. The ratio of their moment of inertia about central axis will be
A) $\rho_{1}:\rho_{2}$
B) $\rho_{1}\rho_{2}:1$
C) $1:\rho_{1}\rho_{2}$
D) $\rho_{2}:\rho_{1}$
Explanation
(d) M.I. of disc $I = \frac{1}{2}MR^{2} = \frac{1}{2}M\left( \frac{M}{\pi\rho t} \right) = \frac{1}{2}\frac{M^{2}}{\pi\rho t}$
$\left( As\ \rho = \frac{Mass}{Volume} = \frac{M}{\pi R^{2}t}\ therefore\ R^{2} = \frac{M}{\pi\ \rho t} \right)$
$\therefore I \propto \frac{1}{\rho}$ [If $M$ and $t$ are constant) $\Rightarrow \frac{I_{1}}{I_{2}} = \frac{\rho_{2}}{\rho_{1}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.