Question

Out of the given bodies (of same mass) for which the moment of inertia will be maximum about the axis passing through its centre of gravity and perpendicular to its plane?

• A. Disc of radius a
• B. Ring of radius a
• C. Square lamina of side 2a
• D. Pour rods of length 2a making a square

Answer 1

Answer: (D)

For disc, $I=\frac{1}{2} m a^{2}$
For ring, $I=m a^{2}$
For square of side $2 a$
$=\frac{M}{12}\left[(2 a)^{2}+(2 a)^{2}\right]=\frac{2}{3} M a^{2}$
For square of rod of length $2 a$
$I=4\left[M \frac{(2 a)^{2}}{12}+M a^{2}\right]=\frac{16}{3} M a^{2}$
Hence, moment of inertia is maximum for square of four rods.