Question

Two uniform circular discs having the same mass and the same thickness but different radii are made from different materials. The disc with the smaller rotational inertia is

• A. the one made from the more dense material
• B. the one made from the less dense material
• C. the disc with the larger angular velocity
• D. the disc with the larger torque

Answer 1

Answer: (A)

Moment of inertia of circular disc $=\frac{1}{2}M{R}^2$
$=\frac{1}{2}M\left(\frac{M}{\pi t\rho }\right)=\frac{1}{2}\frac{M^2}{\pi t\rho }$
$($ As $M=\pi R^{2}t\rho \Rightarrow R^2=\frac{M}{\pi t\rho })$
If mass and thickness are same, then
$I\propto \frac{1}{\rho }$
So, the disc made from more dense material will have smaller rotational inertia.