Question

Consider a uniform wire of mass $M$ and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is:

• A. $\frac{1}{4} \frac{ ML ^{2}}{\pi^{2}}$
• B. $\frac{2}{5} \frac{ ML ^{2}}{\pi^{2}}$
• C. $\frac{ ML ^{2}}{\pi^{2}}$
• D. $\frac{1}{2} \frac{ ML ^{2}}{\pi^{2}}$

Answer 1

Answer: (C)

$\pi r=L$
$ \Rightarrow r=\frac{L}{\pi}$
$I=M r^{2}=\frac{M L^{2}}{\pi^{2}}$