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

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Three identical spherical shells, each of mass m and radius r are placed as shown in the figure. Consider an axis X X ^

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Correct answer: D. 4m r ^ 2

Total moment of inertia of the system, I + I _ 1 + I _ 2 + I _ 3 I _ 2 = I _ 3 = (2)/(3)m r ^ 2 + m r ^ 2 = 5m r ^ 2 3 I _ 1 = (2)/(3)m r ^ 2 &there4; I = 2 × 5 m r ^ 2 3 + (2)/(3)m r ^ 2 I = 12m r ^ 2 3 = 4m r ^ 2

Three identical spherical shells, each of mass m and radius r are...

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