Question

A wire of mass $m$ and length $l$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is :

• A. $m{l}^2$
• B. $\frac{m{l}^2}{4{\pi }^2}$
• C. $\frac{m{l}^2}{2{\pi }^2}$
• D. $\frac{m{l}^2}{8{\pi }^2}$

Answer 1

The correct option is B $\frac{m{l}^2}{4{\pi }^2}$

length is $l$
$l=2\pi r$
$r=\frac{l}{2\pi }$

$I=m{r}^2$

$=\frac{m{l}^2}{4{\pi }^2}$