Diameter of each spherical shell is $R$ and mass $M$ they are joined by a light and massless rod. Calculate the moment of inertia of the system about $x x'$ axis.

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$I_{s y s t e m} = \frac{13}{3} M R^{2}$

$I_{s y s t e m} = 4 M R^{2}$

$I_{s y s t e m} = \frac{2}{3} M R^{2}$

$I_{s y s t e m} = \frac{1}{3} M R^{2}$

answer is C.

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Detailed Solution

$I_{s y s t e m} = \frac{2}{3} M {(\frac{R}{2})}^{2} + [\frac{2}{3} M {(\frac{R}{2})}^{2} + M {(2 R)}^{2}] = \frac{1}{3} M R^{2} + 4 M R^{2} = \frac{13}{3} M R^{2}$

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