Question

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} $

Answer 1

Answer: (D)

Moment of inertia of disc
$I=\frac{1}{2} M R^{2}=\frac{1}{2} M\left(\frac{M}{\pi \rho t}\right)$
$\therefore I=\frac{1}{2} \frac{M^{2}}{\pi \rho t}$
$\left(\right.$ As $\rho=\frac{\text { Mass }}{\text { Volume }}=\frac{M}{\rho R^{2} t}$, therefore, $\left.R ^{2}=\frac{M}{\pi \rho t}\right)$
$\therefore I \propto \frac{1}{\rho}$ (If $M$ and $t$ are constants)
$\Rightarrow \frac{I_{1}}{I_{2}}=\frac{\rho^{2}}{\rho_{1}}$