An object of mass M is divided into two parts ,which are placed at distance d.if gravitational force of attraction is maximum between parts,then find the ratio of mass of both parts

2 answers

If the parts are x and M-x, then

F = Gx(M-x)/r^2
= G/r^2 (Mx-x^2)

This is just a parabola, with vertex at M/2. That is, the force is maximum when the masses are equal.

It's like the area of a rectangle with constant perimeter is greatest if it is a square.
Why we differentiate wrt m?