| Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is: |
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A) \[\frac{137}{15}M{{R}^{2}}\]
B) \[\frac{17}{15}M{{R}^{2}}\]
C) \[\frac{209}{15}M{{R}^{2}}\]
D) \[\frac{152}{15}M{{R}^{2}}\]
Correct Answer: A
Solution :
| \[I=2\left[ \frac{2}{5}M{{R}^{2}}+M4{{R}^{2}} \right]+M\frac{4{{R}^{2}}}{12}\] |
| \[=M{{R}^{2}}\left[ \frac{1}{3}+\frac{4}{5}+8 \right]=\frac{137}{15}M{{R}^{2}}\] |
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