Question

One quarter section is cut from a uniform circular disc of radius R. This section has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

• A. $\frac{1}{2}M{R}^2$
• B. $\frac{1}{4}M{R}^2$
• C. $\frac{1}{8}M{R}^2$
• D. $\sqrt{2}M{R}^2$

Answer 1

The correct option is A

$\frac{1}{2}M{R}^2$

Moment of inertia of complete disc, $I=\frac{1}{2}\left(4M\right)R^2$
So, moment of inertia of quarter disc $=\frac{1}{4}I=\frac{1}{2}M{R}^2$