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

Asked in AIPMT 2015 · Composite and cavity bodies

Figure: Composite and cavity bodies
Answer: (2) 4mr²

Step-by-step solution

Given: three identical thin spherical shells, each m and r; the axis XX' is a diameter of one shell and a tangent to each of the other two.

Idea: a thin shell has I_cm=2/3mr² about a diameter; a tangent axis needs the parallel-axis shift mr².

Shell on the axis: I₁=2/3mr²

Each tangent shell: I=2/3mr²+mr²=5/3mr²

I=2/3mr²+2×5/3mr²=2/3mr²+(10)/3mr²

I=(12)/3mr²=4mr²

Why the other options are wrong

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