Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis ${XX}^{'}$ which is touching the two shells and passing through diameter of the third shell. Moment of inertia of the system consisting of these three spherical shells about $X X^{'}$ axis is:

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Total MI of the system, I = I 1 + I 2 + I 3 I 2 = I 3 = 2 3 m r 2 + m r 2 = 5 m r 2 3 I 1 = 2 3 m r 2 ∴ I = 2 × 5 m r 2 3 + 2 3 m r 2 = 12 m r 2 3 = 4 m r 2

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