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Question

Two identical spheres each of mass M and radius R are separated by a distance 10R. The gravitational force on mass m placed at the midpoint of the line joining the centres of the spheres is:

A
zero
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B
2GMm25R2
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C
GMm25R2
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D
GMm100R2
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Solution

The correct option is A zero
The situation is as shown in the figure.
Let P is the midpoint of the line joining the centers of the spheres.
The gravitational force on mass m due to sphere A is F1=GMm(5R)2along PO1

The gravitational force on mass m due to sphere B is F2=GMm(5R)2along PO2

Net force on mass m is FR=F1F2 (F1 and F2 are opposite in directions)

=GMm(5R)2GMm(5R)2=0

1032397_937485_ans_db77574efb914cffb559920a7a497a0f.png

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