Question

One quarter sector is cut from a uniform circular 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 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

Answer: (A)

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

For complete disc with mass ${}^{\prime }4M^{\prime },M.I.$ about given axis $=\left(4M\right)\left(R^2/2\right)=2M{R}^2$
Hence, by symmetry, for the given quarter of the disc
$M.I.=2M{R}^2/4=\frac{1}{2}M{R}^2$