question_answer

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) \[\frac{2\,M{{L}^{2}}}{3}\]                

B) \[\frac{4\,M{{L}^{2}}}{3}\]

C) \[\frac{5\,M{{L}^{2}}}{3}\]                

D) \[\frac{M{{L}^{2}}}{3}\]

Correct Answer: A

Solution :

Moment of inertia of the system about Z-axis can be found 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 rods 1 and 2 and \[{{l}_{3}}=0\] because rod in lying on Z-axis \[\therefore \,\,\,{{I}_{system}}={{I}_{1}}+{{I}_{2}}+{{I}_{3}}=\frac{M{{L}^{2}}}{3}+\frac{M{{L}^{2}}}{3}+0=\frac{2M{{L}^{2}}}{3}\]