Two solid sphere of same size of a metal are placed in contact by touching each other prove that the gravitational force acting between then is directly proportional to the fourth power of their radius.

Explanation

The weights of the spheres may be assumed to be concentrated at their centres.
So, `F=(G[(4)/(3)piR^(3)rho])xx([(4)/(3)piR^(3)rho])/((2R)^(2))=(4)/(9)[Gpi^(2)rho^(2))R^(4)thereforeFpropR^(4)`