Two uniform circular discs having the same mass and the same thickness but different radii are made from…
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
the one made from the more dense material
the one made from the less dense material
the disc with the larger angular velocity
the disc with the larger torque
Solution
Moment of inertia of circular disc $=\frac{1}{2} M R^2$
$\begin{aligned}
=\frac{1}{2} M\left(\frac{M}{\pi t \rho}\right) & =\frac{1}{2} \frac{M^2}{\pi t \rho} \\
(\text { As } M & \left.=\pi R^2 t \rho \Rightarrow R^2=\frac{M}{\pi t \rho}\right)
\end{aligned}$
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.