If spheres of the same material and same radius r are touching each other, then show that the gravitational force between them is directly proportional to `r^4`.

Explanation

F = `(Gm_1 m_2)/(2r)^2` = `(G4/3 pir^3 rho xx 4/3 pir^3 rho)/(2r)^2` = `4/9 pi^2 rho^2 Gr^4` or `F prop r^4`