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?
(1...x/4
2...×/3
3...×/2
4...2×/3

Answer 1

Answer:

x / 2

Explanation:

Given 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?

Given m1 = 2x, m2 = 3x, d = r

Now let mo be from 3x to 2x

Now m1 = 2x + mo and m2 = 3x – mo

We know that  

F = Gm1m2 / r^2

F = G (2x + mo)(3x – mo) / r^2

F = G/r^2 (6x^2 + 3mox – 2mox – mo^2) / r^2

F = G/r^2 (6x^2 + mo x – mo^2)

Now dF / dmo = 0 and dG/dmo (6x^2 + mox – mo^2) / r^2 = 0 since mo is variable

G / r^2 (0 + x – 2mo) = 0

          2mo = x

 Therefore mo = x/2