Question

Four identical thin rods each of mass M and length l, from a squre frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

• A. $\frac{2}{3}M{l}^2$
• B. $\frac{13}{3}M{l}^2$
• C. $\frac{1}{3}M{l}^2$
• D. $\frac{4}{3}M{l}^2$

Answer 1

The correct option is D $\frac{4}{3}M{l}^2$

Moment of inertia of rod of mass M and length l through an axis perpendicular to length = $\frac{M{l}^2}{3}$
∴ for all four rods, $I=4\left(\frac{M{L}^2}{3}\right)=\frac{4}{3}M{l}^2.$