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Question

# Two spheres each of mass M and radius R/2 are connected with a massless rod of length 2R as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod:

A
215MR2
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B
25MR2
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C
52MR2
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D
521MR2
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Solution

## The correct option is A 215MR2Moment of Inertia of A about PQ= IA=25M(R2)2=110MR2Moment of Inertia of B about its own axis= IB=25M(R2)2=110MR2Using parallel axis theoremMoment of Inertia of B along PQ= IBPQ=M(2R)2+110MR2=4110MR2Moment of Inertia of system is I=IA+IBPQ=110MR2+4110MR2=2110MR2

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