1.

Two sphere each of mass M and radius - are2connected with a massless rod of length 2R asshown in the figure. What will be the moment ofinertia of the system about an axis passingthrough the centre of one of the spheres andperpendicular to the rod:R/2R/2

Answer»

Moment of inertia of sphere A about the axis PQ is, IA= (2/5)M(R/2)2= (1/10)MR2

Moment of inertia of sphere B about its own axis is, IB= (2/5)M(R/2)2= (1/10)MR2

Using parallel axes theorem the moment of inertia of sphere B about the axis PQ is, IB/= M(2R)2+ (1/10)MR2= (4 + 1/10)MR2= (41/10)MR2

So, moment of inertia of the system is, I = IA+ IB/= (1/10)MR2+ (41/10)MR2

=> I = (42/10)MR2= (21/5)MR2



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