# Gravitation problem

1. Apr 6, 2009

### awri

1. The problem statement, all variables and given/known data
If a uniform sphere of mass M and radius R, is height h above an infinite sheet of uniform density $$\rho$$$$_{s}$$, what is the gravitational force of the sphere, on the sheet.

2. Relevant equations
F=$$\frac{GMm}{R^{2}}$$; $$\Phi$$=$$\frac{GM}{R}$$; $$\nabla$$$$\bullet$$g=4$$\pi$$G$$\rho$$; U=m$$\Phi$$; F=-$$\nabla$$U

3. The attempt at a solution
My professor advised me to find the force of the sheet on the sphere since that force would be equal to the force of the sphere on the sheet. So I drew a gaussian cylinder around my "sheet" and attempted to calculate g by saying that $$\nabla$$$$\bullet$$g = $$\frac{dg}{dz}$$ since all relavent field lines were in the z direction. All I think I need to know is whether or not that was the correct assumption. I dont think it is because it yeilds an answer that looks like 4$$\pi$$G$$\rho$$z. And the z is an issue. the answer in the back of the book is 2$$\pi$$GM$$\rho$$. Any help would be much appreciated.

2. Apr 6, 2009

### Redbelly98

Staff Emeritus
There is another way to use the gaussian cylinder. There's an equation that relates the surface integral of dA over the cylinder, to the mass within the cylinder. I think that will be useful here.