Question

One quarter sector is cut from a uniform disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the center 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 $\frac{1}{2}M{R}^2$

Let whole mass of disc $=4M$
Hence, moment of inertia of the disc about given axis = $\frac{1}{2}\left(4M\right)R^2=2M{R}^2$
Therefore, moment of inertia of quarter section
$=\frac{1}{4}\left(2M{R}^2\right)=\frac{M{R}^2}{2}$