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Question

Two identical spheres are placed in contact with each other. If their radii are varied keeping their mass constant, find the relation between gravitational attraction F and radius of the spheres R. Assume the radii of both the spheres to be identical at all instances.

A

FR2

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B

FR4

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C

F1R2

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D

F1R4

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Solution

The correct option is C

F1R2


The two identical spheres behave as point masses with all the mass concentrated at the centre.
Given radius of each sphere is R. Since the two spheres are kept in contact with each other, the distance between their centres is 2R.

According to the universal law of gravitation, the gravitational force between two bodies is inversely proportional to the square of the distance between them.
F14R2
Since '4' is a constant, we can write, F1R2

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