Question

At what point would you need to place a sphere of mass = M + radius = Rnbetween two spheres in order to create a zero net force on the sphere if the second sphere has a mass =2M and a radius=3R + the third sphere has a mass of 3M and a radius of 2/3 R. Assume the distance between the spheres 2 + 3 is 10R

Answer 1

equate the two gravitational forces

Answer 2

so Gm1m2/r^2=Gm1m3/R^2, where r is the distance between the COM of sphere 1/2 and R is the distance between COM of spheres 1/3

Answer 3

so to find the answer, put r as an unknown and R as (10-r)

Answer 4

This is still not making much sense..