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. $\frac{2ML^{2}}{3}$
• B. $\frac{4ML^{2}}{3}$
• C. $\frac{5ML^{2}}{3}$
• D. $\frac{ML^{2}}{3}$

Answer 1

Answer: (A)

$\frac{2ML^{2}}{3}$

Answer 2

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

$I_{1} = I_{2} = \frac{ML^{2}}{3}$ because z-axis is the edge of rod 1 and 2 and $I_{3} = 0$ because rod in lying on z-axis

$\therefore$ $I_{\text{system}} = I_{1} + I_{2} + I_{3} = \frac{ML^{2}}{3} + \frac{ML^{2}}{3} + 0 = \frac{2ML^{2}}{3}$.