Q. Two discs have same mass and thickness. Their materials have densities $d_{1}$ and $d_{2}$. The ratio of their moments of inertia about central axis will be
A) $d_{1}:d_{2}$
B) $d_{1}\ d_{2}\ :1$
C) $1\ :d_{1}\ :d_{2}$
D) $d_{2}\ :d_{1}$
Explanation
(d) As $m_{1} = m_{2}\ \ \ \therefore\pi R_{1}^{2}xd_{1} = \pi R_{2}^{2}xd_{2}$
$\frac{R_{1}^{2}}{R_{2}^{2}} = \frac{d_{2}}{d_{1}}$
Now, $\frac{I_{1}}{I_{2}} = \frac{\frac{1}{2}mR_{1}^{2}}{\frac{1}{2}mR_{2}^{2}} = \frac{R_{1}^{2}}{R_{2}^{2}} = \frac{d_{2}}{d_{1}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.