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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:
1033948_051643ad08b44f619ae3dc66e221e720.PNG

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 215MR2
Moment of Inertia of A about PQ= IA=25M(R2)2=110MR2

Moment of Inertia of B about its own axis= IB=25M(R2)2=110MR2
Using parallel axis theorem
Moment of Inertia of B along PQ=
IBPQ=M(2R)2+110MR2=4110MR2

Moment of Inertia of system is
I=IA+IBPQ=110MR2+4110MR2=2110MR2

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