Physics - Rotation Question with Solution | TestHub

The system consists of three rods placed along the X, Y, and Z axes, each with one end at the origin.

The moment of inertia of the rod along the X-axis about the Z-axis (which is perpendicular to the rod and passes through its end) is $I_1=\frac{M{L}^2}{3}$.

The moment of inertia of the rod along the Y-axis about the Z-axis (which is also perpendicular to the rod and passes through its end) is $I_2=\frac{M{L}^2}{3}$.

The moment of inertia of the rod along the Z-axis about the Z-axis is $I_3=0$, since the axis passes through the rod itself and its thickness is negligible.

The total moment of inertia of the system about the Z-axis is the sum of the individual moments of inertia:

$I=I_1+I_2+I_3$

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

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