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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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3 m r^{2}

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

4 m r^{2}

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

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detailed solution

Correct option is C

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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Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX1 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 XX1 axis is:

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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: