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Question

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



A
13715MR2
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B
1715MR2
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C
20915MR2
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D
15215MR2
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Solution

The correct option is A 13715MR2
For ball, using parallel axes theorem,for ball moment of inertaia,
Iball=25MR2+M(2R)2=225MR2

For two balls 2Iball=2×225MR2

For rod
Irod=M(2R)212=MR23

Moment of inertia of the system is
Isystem=2Iball+Irod
445MR2+MR23=13715MR2

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