Question

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

• A. A disk of radius a
• B. A ring of radius a
• C. A square lamina of side 2a
• D. Four rods forming a square of side 2a

Answer 1

The correct option is D Four rods forming a square of side 2a

MI of disk of radius $a$ about given axis is $m{a}^2/2$

MI of ring of radius $a$ about given axis is $m{a}^2$

MI of square of side $2a$ about given axis is $m(2a{)}^2/6=2m{a}^2/3$

MI of four rods forming square of side $2a$ about given axis is $4\times m(2a{)}^2/12+m{a}^2=4m{a}^2/3$

So among all options four rods forming square of side $2a$ has highest moment of inertia of $4m{a}^2/3$ about an axis passing through its center of mass and perpendicular to the plane of body.