Question

A thin uniform wire of mass $m$ and length $l$ is bent into a circle. The moment of inertia of the wire about an axis passing through its one end and perpendicular to the plane of the circle is

• A. $\frac{2 mL^{2}}{\pi^{2}}$
• B. $\frac{mL^{2}}{\pi^{2}}$
• C. $\frac{mL^{2}}{2\pi^2}$
• D. $\frac{mL^{2}}{3\pi^2}$

Answer 1

Answer: (C)

$2 \pi r=L$
$r=\frac{L}{2 \pi},\,\, I=2 m r^{2}=2 m\left(\frac{L}{2 \pi}\right)^{2}$