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Question

Find the distance between the centre of gravity and centre of mass of a two-particle system attached to the ends of a light rod. Each particle has the same mass. Length of the rod is R, where R is the radius of the earth.

42028_030fb193362844b19fff2f4d05ba1d41.png

A
R
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B
R2
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C
zero
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D
R4
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Solution

The correct option is B R2
The centre of gravity of the Earth lie at its centre (Point p in picture)
The centre of mass of the rod is mR+m.02m=R2
The distance between CM of the rod and CG of the Earth is=R2 [PS=R2 in the picture]

1128844_42028_ans_aa431faed9f647ca82b8c4f078c31942.png

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