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

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$3 {mr}^{2}$

$\frac{16}{5} {mr}^{2}$

$\frac{11}{5} {mr}^{2}$

$4 {mr}^{2}$

answer is C.

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Detailed Solution

Moment of inertia for one of the hollow sphere is through it's natural axis.

And for the other two we can find by using parallel axis theorem.

And the axis XX' is at a distance of r from its natural axis.

$I_{{XX}^{'}} = \frac{2}{3} m r^{2} + 2 [\frac{2}{3} m r^{2} + m r^{2}] = \frac{2}{3} m r^{2} + \frac{10}{3} m r^{2} = 4 m r^{2}$

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