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Question

A uniform ring of mass m is lying at a distance 1.73a from the centre of a sphere of mass M just over the sphere where a is the small radius of the ring as well as that of the sphere. Then, the gravitational force exerted by one on the other is
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A
GMm8a2
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B
GMm(1.73a)2
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C
3GMma2
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D
1.73GMm8a2
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Solution

The correct option is A 1.73GMm8a2
In this case the expression of gravitational force is F=GMmr(r2+R2)32
here, r=1.73a,R=a
F=GMm1.73a(2.99a2+a2)32=GMm1.73aa3(4)32=1.73GMm8a2(take 2.993)

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