Question

$I$ is the moment of inertia of a thin circular plate about an axis of rotation perpendicular to the plane of plate and passing through its centre. The moment of inertia of same plate about an axis passing through its diameter is :

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

Answer 1

The correct option is D $\frac{I}{2}$

$I_2$ and $I_3$ are MOI about axis passing through the diameter.
Using symmetry, we know that,
$I_2=I_3$
By perpendicular axis theorem,
$I_1=I_2+I_3$
$I_1=2I_2$
$\frac{I_1}{2}=I_2$