Question

Four rods each of mass $m$ form a square having length of diagonal $b$, rotates about its diagonal. Its moment of
inertia is $\frac{pm{b}^2}{18}$ . Find $p$.

Answer 1

We know that, M.I along an axis perpendicular to a rod along one of its ends is
$I_{COM}=\frac{m{b}^2}{3}$
For 4 rods, $\frac{4m{b}^2}{3}$
Therefore, M.I. of the square about an axis along one of the diagonals is:
$M.I.=4\frac{m{b}^2}{3}{\sin }^2{45}^o$
$=\frac{2m{b}^2}{3}$
Also, M.I. given in this case = $\frac{pm{b}^2}{18}$
Therefore,
$\frac{pm{b}^2}{18}$ $=\frac{2m{b}^2}{3}$

Final Answer: p = 12