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(A) The moment of inertia of the system about the $Z$-axis is the sum of the moments of inertia of the individual rods about the $Z$-axis.$1$. For the

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

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(A) The moment of inertia of the system about the $Z$-axis is the sum of the moments of inertia of the individual rods about the $Z$-axis.$1$. For the rod along the $X$-axis (rod $1$): The $Z$-axis is perpendicular to the rod at its end. Therefore,its moment of inertia is $I_1 = \frac{ML^2}{3}$.$2$. For the rod along the $Y$-axis (rod $2$): The $Z$-axis is perpendicular to the rod at its end. Therefore,its moment of inertia is $I_2 = \frac{ML^2}{3}$.$3$. For the rod along the $Z$-axis (rod $3$): The rod lies along the $Z$-axis itself. Therefore,the distance of every mass element from the $Z$-axis is zero,so $I_3 = 0$.$4$. The total moment of inertia of the system is $I_{	ext{system}} = I_1 + I_2 + I_3 = \frac{ML^2}{3} + \frac{ML^2}{3} + 0 = \frac{2ML^2}{3}$.

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 rod is at the origin. The moment of inertia of this system about the $Z$-axis is

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