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 the body?

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

Answer 1

Answer: (D)

$I _{\text {disc }}=\frac{M a^{2}}{2}$,
$ I_{\text {ring }}=M a^{2}$
$I _{\text {squse lienira }} =M\left[\frac{l^{2}+b^{2}}{12}\right]=\frac{M\left(a^{2}+a^{2}\right)}{12}$
$=\frac{2 M a^{2}}{12}=\frac{M a^{2}}{6}$
$ I_{\text {Four rods }}=\left[\frac{M a^{2}}{12}+\frac{M a^{2}}{4}\right] \times 4=\frac{4}{3} M a^{2}$
$ I_{\text {square }}=\frac{4 M a^{2}}{3} \times 4=\frac{16}{3} M a^{2} $