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Question

If distance between the two masses is reduced to one-fourth of the initial value, then force of gravitation between them becomes ____ of the initial value.

A
4 times
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B
8 times
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C
16 times
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D
2 times
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Solution

The correct option is C 16 times
Let M1 and M2 be the masses of two objects and R be the distance between them.
The gravitational force, F=GM1M2R2, where G is the universal gravitational constant.

Since M1,M2 and G are constants,
F1R2

Let the force when distance is reduced to one-fourth be F
FF=1/(R4)21/R2
FF=16/R21/R2
FF=16F=16F
Hence, the gravitational force becomes 16 times of the initial value.

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