Q. Two discs of the same material and thickness have radii $0.2\ m$ and $0.6\ m$. Their moments of inertia about their axes will be in the ratio
A) $1\ :81$
B) $1\ :27$
C) $1\ :9$
D) $1\ :3$
Explanation
(a) $I = \frac{1}{2}MR^{2} = \frac{1}{2} \times (\pi R^{2}t \times \rho) \times R^{2}$
$\Rightarrow I \propto R^{4}$ (As $t$ and $\rho$ are same)
$\therefore\frac{I_{1}}{I_{2}} = \left( \frac{R_{1}}{R_{2}} \right)^{4} = \left( \frac{0.2}{0.6} \right)^{4} = \frac{1}{81}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.