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If the distance between masses of two object is increased by five times, by what factor would the mass of one of them have to be changed to maintain the same gravitational force? Would there be an increase or decrease in the same?
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If the distance between masses of two object is increased by five time...
Let the objects be placed at a separation r and let their masses be m1 and m2.
Let gravitational force between the objects be F.
F = G . m1 . m2 / r^2(G is the gravitational constant = 6.674 x 10^-11 N m^2 kg^-2)
When r is increased by 5 times, let m1 be increased by k times to maintain the same gravitational force between the objects.
Let F1 = G . km1 . m2 / (5r)^2
= G . km1 . m2 / 25 . r^2
Since F = F1,
G . km1 . m2 / 25 . r^2 = G . m1 . m2 / r^2
Solving the above equation, we get k=25.
Thus the mass of one of the objects would have to be increased 25 times.
(The dots are all multiplication symbols)

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