If the distance between two masses is increased by a factor of 4, by what factor would the mass of one of them have to be altered to maintain the same gravitational force

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Solution

The gravitational force b/w two bodies having mass M and m and separated by a distance r is denoted as

F = GMm/r²

When r is increased by factor 4 , then its effect will be indirectly proportional and in square , means G force will lessened by 16 times ….For compensating this, one of the body needed to be heavier by 16 times

Hence answer is 16

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