A) \[\frac{16}{5}m{{r}^{2}}\]
B) \[4m{{r}^{2}}\]
C) \[\frac{11}{5}m{{r}^{2}}\]
D) \[3m{{r}^{2}}\]
Correct Answer: B
Solution :
[b]: Net moment of inertia of the system, \[I={{I}_{1}}+{{I}_{2}}+{{I}_{3}}\] The moment of inertia of a shell about its diameter,\[{{I}_{1}}=\frac{2}{3}m{{r}^{2}}\] The moment of inertia of a shell about its tangent is given by \[{{I}_{2}}={{I}_{3}}={{I}_{1}}+m{{r}^{2}}=\frac{2}{3}m{{r}^{2}}+m{{r}^{2}}=\frac{5}{3}m{{r}^{2}}\] \[\therefore \]\[I=2\times \frac{5}{3}m{{r}^{2}}+\frac{2}{3}m{{r}^{2}}=\frac{12m{{r}^{2}}}{3}=4m{{r}^{2}}\]
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