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.