Question

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?

Answer 1

Gravitational force (F), distance between two masses (r) and mass of both (m1 and m2) are related as

F ∝ m1m2 / r^2

If Distance (r) is increased by 4 then F is decreased by 4^2 = 16.
To neutralise this effect product of masses m1 and m2 should be equal to 16.

Hence mass of any one object should increase to 16 times that of its initial.

Answer 2

Answer:

here’s an inverse squared relationship between gravitational force and the distance between the two objects, due to the equation

Fg=$\frac{gm1m2}{r^{2} }$

Hence, if the distance is increased by a factor of 6, we get a factor of  136 . Therefore, the product of the two masses needs to increase by a factor of 36, which we can do by increasing the mass of each object by a factor of 6.

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