# Hard gravitational force problem

1. Nov 13, 2007

### alexwaylo2008

Hard gravitational force problem!!

1. The problem statement, all variables and given/known data
Derive an expression for the gravitational force between a sphere with mass m and another sphere with mass M and radius R, IF the sphere of mass M has a spherical hollow inside which touches the surface of the sphere and the center of the sphere. The distance between M and m is d (including the radius R and ignoring the radius of m).

2. Relevant equations
F = GMm/r^2

3. The attempt at a solution
I tried to calculate the volume of the sphere with the hollow and I got = 7piR^3/6, but then I don't know what to do. The answer is supposed to be:
F = (GMm/d^2)( 1 - 1/(8(1-R/2d)^2))

Last edited: Nov 13, 2007
2. Nov 13, 2007

### Astronuc

Staff Emeritus
Find the gravitational force between mass M and m without the hole.

Then find the gravitational force of the mass that would be in the hole, and subtract it from the other force found above. Think superposition of vectors.

If d is the distance between m and M (center), what is the distance between m and the hole in M? That is the key.