Question

Moment of inertial of a circular wire of mass $M$ and radius $R$ about its diameter is

• A. $M{R}^2/2$
• B. $M{R}^2$
• C. $2M{R}^2$
• D. $M{R}^2/4$

Answer 1

The correct option is A $M{R}^2/2$

Moment of inertia of circular wire about an axis passing through the centre and perpendicular to the plane, $I_z=M{R}^2$

Using perpendicular axis theorem, $I_z=I_x+I_y$ where $I_x$ and $I_y$ are the MOI about diameter.

As in this case, $I_x=I_y$

$I_z=2I_x$

$⟹I_x=\frac{1}{2}M{R}^2$