Question

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

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

Answer 1

Answer: (D)

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 $2 a$ about given axis is $m \left(\right. 2 a \left.\right)^{2} / 6 = 2 m a^{2} / 3$
MI of four rods forming square of side $2 a$ about given axis is $4 \times m \left(\right. 2 a \left.\right)^{2} / 12 + m a^{2} = 4 m a^{2} / 3$
So among all options four rods forming square of side $2 a$ has highest moment of inertia of $4 m a^{2} / 3$ about an axis passing through its center of mass and perpendicular to the plane of body.