Question

$\text{MOI}$ of a circular ring of radius $R$ about the line passing through its centre of mass in the plane of circle is $I$. Find the $\text{MOI}$ of ring about a line passing through its $\text{COM}$ and perpendicular to its plane.

• A. $I$
• B. $\frac{I}{2}$
• C. $\frac{I}{4}$
• D. $2I$

Answer 1

The correct option is D $2I$

The axis i.e. $z-$axis passing through $\text{COM}$ are as shown in the below figure.

As we know from perpendicular axis theorem,
$I_Z=I_X+I_Y$
Given, $I_X=I_Y=I$
$\Rightarrow I_Z=I+I=2I$