Question

Moment of inertia of a disc about a diameter is I. Find the moment of inertia of disc about an axis perpendicular to its plane and passing through its rim ?

• A. 6 I
• B. 4 I
• C. 2 I
• D. 8I

Answer 1

The correct option is A 6 I

Moment of inertia of a disc about an axis passing through center and perpendicular to plane of the disc=$\frac{1}{2}M{R}^2$.

Thus moment of inertia about a diameter of the disc=$\frac{1}{2}\times \frac{1}{2}M{R}^2=\frac{1}{4}M{R}^2=I$

$⟹M{R}^2=4I$

Using parallel axis theorem,
$I_d=I_{CM}+M{d}^2=\frac{1}{2}M{R}^2+M{R}^2=\frac{3}{2}M{R}^2=6I$