First slide

Moment of intertia

Question

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

Moderate

A

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

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

3 ${mr}^{2}$
D

4 ${mr}^{2}$

Solution

$I = I_{A} + I_{B} + I_{C}$
= $(\frac{2}{3} {mr}^{2} + {mr}^{2}) + (\frac{2}{3} {mr}^{2} + {mr}^{2}) + \frac{2}{3} {mr}^{2}$
= 4 ${mr}^{2}$

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