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:

Question

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:, 11 5 m r 2, 3 m r 2, 16 5 m r 2, 4 m r 2

MARKS App · Accepted Answer

​​​​​​​ 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 = 5 m r 2 3 I 1 = 2 3 m r 2 ∴ I = 2 × 5 m r 2 3 + 2 3 m r 2 I = 12 m r 2 3 = 4 m r 2

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