question_answer

Three thin 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 rods is at the origin. The moment of inertia of this system about Z-axis is:

A) \[~2\text{ }M{{L}^{2}}/3\]             

B) \[~4\text{ }M{{L}^{2}}/3\]

C) \[~5\text{ }M{{L}^{2}}/3\]             

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

Correct Answer: A

Solution :

\[{{I}_{2}}={{I}_{1}}+{{I}_{2}}+{{I}_{3}}=\frac{M{{L}^{2}}}{3}+\frac{M{{L}^{2}}}{3}+o=\frac{2M{{L}^{2}}}{3}\] This is because z-axis is passing through one end of each of two rods aligned along  and y-axes. Hence, the correction option is [a].