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 A215MR2 According to parallel axis theorem,
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 I=25M(R2)2+M(2R)2+25M(R2)2=4MR2+15MR2=215MR2 ∴(a)