Question

The moment of inertia of a system of four rods, each of length $l$ and mass $m$, about the axis shown is

• A. $\frac{2}{3} m l^{2}$
• B. $2 m l^{2}$
• C. $3 m l^{2}$
• D. $\frac{8}{3} m l^{2}$

Answer 1

Answer: (D)

Moment of inertia about $2:$
$I_{2}=4\left(\frac{m l^{2}}{3} \sin ^{2} 45^{\circ}\right)=\frac{2 m l^{2}}{3}$
Apply perpendicular axis theorem,
$I_{1} =I_{2}+m h^{2} $
$=\frac{2 m l^{2}}{3}+4 m\left(\frac{1}{\sqrt{2}}\right)^{2}=\frac{8}{3} m l^{2}$