Question

Four thin rods each of mass $m$ and length $l$ are joined to make a square. If the moment of inertia of all the four rods about any side of the square is $\frac{x}{3}m{l}^2$, find the value of $x$.

Answer 1

$I=I_1+I_2+I_3+I_4$
$=0+\frac{m{l}^2}{3}+m{l}^2+\frac{m{l}^2}{3}$
$=\frac{5}{3}m{l}^2$