If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of them have to be altered to maintain the same gravitational force? Would this be an increase or decrease in the mass?

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Solution

Gravitational force is given by

F= GMm/r^2

That implies Force is inversely proportional to the square of the distance between the objects.

Therefore, If the distance between the objects increased 5 times,force will decrease by a factor of 25.
therefore to balance this by changing one of the mass,it should multiply with 25.
That is, ' m' should be changed to '25×m'.

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