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Question

Two spheres each of mass M and radius R2 are connected with a massless rod of length R as shown in the figure. The moment of inertia of the system about an axis (YY) passing through the centre of one of the spheres and perpendicular to the rod is

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
According to parallel axis theorem, I=Io+Md2
Momemt of inertia of farthest sphere is I1=25M(R2)2+M(2R)2
Momemt of inertia of nearest sphere is I2=25M(R2)2
Momemt of inertia of massless rod is I3=0
Moment of inertia of system is given by, I=I1+I2+I3
I=25M(R2)2+M(2R)2+25M(R2)2=4MR2+15MR2=215MR2.


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