Physics - Rotation Question with Solution | TestHub

Mass of each rod $m=2M$, length $=L$.

Moment of inertia of the system about the $x$-axis is the sum of the moments of inertia of the three rods about the $x$-axis.

$I_x=I_1+I_2+I_3$

For the rod along the $x$-axis, the distance of any mass element from the $x$-axis is zero.

$I_1=0$

For the rod along the $y$-axis, the $x$-axis is perpendicular to it and passes through its end.

$I_2=\frac{m{L}^2}{3}=\frac{(2M)L^2}{3}=\frac{2M{L}^2}{3}$

For the rod along the $z$-axis, the $x$-axis is perpendicular to it and passes through its end.

$I_3=\frac{m{L}^2}{3}=\frac{(2M)L^2}{3}=\frac{2M{L}^2}{3}$

Total moment of inertia:

$I_x=0+\frac{2M{L}^2}{3}+\frac{2M{L}^2}{3}=\frac{4M{L}^2}{3}$

Answer: $\frac{4{\mathrm{ML}}^2}{3}$