Q. Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio
A) 1 : 3
B) 3 : 1
C) 1 : 9
D) 9 : 1
Explanation
(b) M.I. of disc $= \frac{1}{2}MR^{2} = \frac{1}{2}M\left( \frac{M}{\pi t\rho} \right) = \frac{1}{2}\frac{M^{2}}{\pi t\rho}$
$\left( As\ \rho = \frac{M}{\pi R^{2}t}\ There\ fore\ R^{2} = \frac{M}{\pi\ t\rho} \right)$
If mass and thickness are same then, $I \propto \frac{1}{\rho}$
$\therefore\frac{I_{1}}{I_{2}} = \frac{\rho_{2}}{\rho_{1}} = \frac{3}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.