Three identical spheres,each of mass M and ra | vedclass

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(C) The system consists of three identical spheres of mass $M$ and radius $R$. Let the top sphere be $S_1$ and the two bottom spheres be $S_2$ and $S_

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$\frac{16}{5} M R^2$

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(C) The system consists of three identical spheres of mass $M$ and radius $R$. Let the top sphere be $S_1$ and the two bottom spheres be $S_2$ and $S_3$.$1$. For the top sphere $S_1$,the axis $XX'$ passes through its center (diameter). The moment of inertia of a solid sphere about its diameter is $I_1 = \frac{2}{5} M R^2$.$2$. For the bottom spheres $S_2$ and $S_3$,the axis $XX'$ is tangent to them. The distance from the center of each bottom sphere to the axis $XX'$ is $R$. Using the parallel axis theorem,$I = I_{cm} + Md^2$,where $I_{cm} = \frac{2}{5} M R^2$ and $d = R$.So,$I_2 = I_3 = \frac{2}{5} M R^2 + M R^2 = \frac{7}{5} M R^2$.$3$. The total moment of inertia of the system about $XX'$ is $I_{total} = I_1 + I_2 + I_3$.$I_{total} = \frac{2}{5} M R^2 + \frac{7}{5} M R^2 + \frac{7}{5} M R^2 = \frac{16}{5} M R^2$.

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