Question

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

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

Answer 1

Answer: (D)

$\frac{4}{3}Ml^2$

Answer 2

$I =4 \times\left[\frac{ M \ell^{2}}{12}+ M \left(\frac{\ell}{2}\right)^{2}\right]$
the parallel axis theorem $=\frac{4}{3} M \ell^{2}$