Question

Moment of inertia of ring about any of diameters is $I_0$. Find the moment of inertia of ring about any point on its circumference and perpendicular to its plane.

• A. $I_0$
• B. $2I_0$
• C. $3I_0$
• D. $4I_0$

Answer 1

The correct option is D $4I_0$

$I_0$ is Moment of inertia about diameter
$I_c$ is moment of Inertia through centre and perpendicular to plane of ring
$I_p$ is moment of Inertia through circumference and perpendicular to plane of ring
$I_0=\frac{I_{\text{c}}}{2}=\frac{M{R}^2}{2}$
$\Rightarrow I_{\text{c}}=2I_0=M{R}^2$

By Parallel axis theorem
$I_{\text{p}}=I_{\text{c}}+M{R}^2=4I_0$