Three thin rods,each of length L and mass M,a | vedclass

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(A) Let the three rods be $R_1, R_2,$ and $R_3$ along the $x, y,$ and $z-$ axes respectively.$1$. For rod $R_1$ (along the $x-$ axis): The moment of i

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

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(A) Let the three rods be $R_1, R_2,$ and $R_3$ along the $x, y,$ and $z-$ axes respectively.$1$. For rod $R_1$ (along the $x-$ axis): The moment of inertia about the $z-$ axis is the same as the moment of inertia about the $y-$ axis,which is $I_1 = \frac{ML^2}{3}$.$2$. For rod $R_2$ (along the $y-$ axis): The moment of inertia about the $z-$ axis is the same as the moment of inertia about the $x-$ axis,which is $I_2 = \frac{ML^2}{3}$.$3$. For rod $R_3$ (along the $z-$ axis): Since the rod lies along the axis of rotation ($z-$ axis),every point on the rod is at a distance $r = 0$ from the axis. Thus,its moment of inertia is $I_3 = 0$.$4$. The total moment of inertia of the system about the $z-$ axis is $I = I_1 + I_2 + I_3 = \frac{ML^2}{3} + \frac{ML^2}{3} + 0 = \frac{2ML^2}{3}$.

Three thin rods,each of length $L$ and mass $M$,are placed along the $x, y,$ and $z-$ axes such 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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