Two identical copper spheres with uniform density each of radius R are in contact with each other. If the gravitational attraction between them is F, then
Mass=density × volume
Let M be the mass and ρ be the density of each sphere.
Volume of each sphere =43πR3,
where R is the radius of the sphere.
So, the mass of each sphere is 43πR3ρ
The distance between their centres is 2R.
So, the force of attraction between them is F=GM2(2R)2,
where G is the universal gravitational constant.
∴F=G(43πR3ρ)(43πR3ρ)1(2R)2
⟹F∝R6R2
⟹F∝R4