Question

Three rods each of length L and mass M are placed along X, Y and Z-axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about Z axis is.

• A. $\frac{2M{L}^2}{3}$
• B. $\frac{4M{L}^2}{3}$
• C. $\frac{5M{L}^2}{3}$
• D. $\frac{7M{L}^2}{3}$

Answer 1

The correct option is A $\frac{2M{L}^2}{3}$

Moment of inertia of the system about z-axis can be find out by calculating the moment of inertia of individual rod about z-axis
$I_1=I_2=\frac{M{L}^2}{3}$ because z-axis is the edge of rod 1 and 2
and $I_3=0$ because rod in lying on z-axis
$\therefore I_{System}=I_1+I_2+I_3=\frac{M{L}^2}{3}+\frac{M{L}^2}{3}+0=\frac{2M{L}^2}{3}.$