Question

Two point objects of mass 2x and 3x are separated by a distance r keeping the distance fixed, how much
mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum​

Answer 1

Let the amount of mass transferred be m and new force be F.

F=G(3x-m)(2x+m)/r^2

F=G(6x^2 + mx - m^2)

For force to be maximum,

dF/dm = 0

d(G(6x^2 + mx - m^2)/r^2)/dy = 0

x - 2m = 0

-2m = -x

m=x/2