Question

For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of body?

• A. a ring of radius $l$
• B. a disc of radius $l$
• C. a square lamina of side $2l$
• D. four rods forming square of side $2l$

Answer 1

The correct option is D four rods forming square of side $2l$

Moment of inertia of ring of radius, $l=m{l}^2$
Moment of inertia of disc of radius, $l=\frac{m{l}^2}{2}$
Moment of inertia of square lamina of side length, $2l=\frac{2m{l}^2}{3}$
Moment of inertia of square foremed by four rods of length, $2l=\frac{4m{l}^2}{3}$.
Therefore, moment of inertia of four rods forming square of length $2l$ is larger.