Two identical copper spheres of radius `R` are in contact with each other. If the gravitational attraction between them is `F`, find the relation between `F` and `R`.

Explanation

Let `M` be the mass of each copper sphere,
and `rho` be the density of copper. Then ,
`M = (4)/(3) pi R^(3). rho`
Gravitational attraction between the two spheres is
`F = (GMM)/((2R)^(2)) = (GM^(2))/(4R^(2)) = (G)/(4R^(2)) xx ((4)/(3) pi R^(3) rho)^(2)`
`= (4)/(9) pi^(2) G rho^(2) R^(4)`
i.e., `F prop R^(4)` if `rho` is constant.
It is not correct becouse the gravitational force obeys inverse square law and is related with masses and not with density. So `F prop 1//R^(2)` is correct answer.