Consider the limit on increasing the gravitational force by bringing the masses closer together. The two spheres of osmium cannot have their centers closer than the sum of their radii, and if the radii are made smaller, the masses decrease. To what power of the radius r is the mass of each sphere proportional?

Question

In proportion to what power of r does the smallest separation of the sphere centers vary?


So the attraction between the spheres of maximum mass at smallest separation increases as r to what power?

Answer 1

force= GMm/r^2 but you want m=kr^3 and M = kr^3 because mass is proportional to volume (assuming the radi is the same on each sphere).

force=Gk^2(r^6/r^2)=Constant*r^4