Question

A thin wire of mass $ M $ and length $ L $ is bent to form a circular ring. The moment of inertia of this ring about its axis is

• A. $ \frac{1}{4\pi^{2}} \,ML^{2} $
• B. $ \frac{1}{12} \, ML^{2} $
• C. $ \frac{1}{3\pi^{2}} \,ML^{2} $
• D. $ \frac{1}{\pi^{2}} \, ML^{2} $

Answer 1

The Correct Option is A

Here, a thin wire of length $L$ is bent to form a circular ring

Then, $2\pi r=L$ [$r$ is the radius of ring]
$\Rightarrow r=\frac{L}{2\pi}$
Hence, the moment of inertia of the ring about its axis
$I=Mr^{2} \Rightarrow I=M \left(\frac{L}{2\pi}\right)^{2}$
$\Rightarrow I=\frac{ML^{2}}{4\pi^{2}}$