Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis $X X^{1}$ which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about $X X^{1}$ axis is:

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$\frac{16}{5} m r^{2}$

$\frac{11}{5} m r^{2}$

$3 m r^{2}$

$4 m r^{2}$

answer is C.

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Detailed Solution

Moments of inertia of the shells about the given axis are

$I_{1} = \frac{2}{3} m r^{2};$

$I_{2} = I_{3} = \frac{2}{3} m r^{2} + m r^{2} = \frac{5}{3} m r^{2}$ ........by parallel axis theorem

$I = I_{1} + I_{2} + I_{3}$

$I = 4 m r^{2}$

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