Gravitational potential and equilibrium of a thin ring

1. Dec 4, 2007

DieCommie

1. The problem statement, all variables and given/known data
Consider a thin ring of radius a and mass M. A mass m is placed in the plane of the ring (not in the center!). Determine the gravitational potential for r < a. Find a position of equilibrium and determine whether it is stable or unstable. (Hint: Consider a small displacement from the equilibrium position and do an expansion.)

2. Relevant equations

3. The attempt at a solution
I drew the picture and tried to figure some sort of integral using law of cosines. I couldnt quite get any where with that though... I wonder if this is an application of Stokes' Theorem?

Any tips on which direction would be great!!
Thanks

2. Dec 5, 2007

Gokul43201

Staff Emeritus
Some clarifications seem to be in order: What is r? Does the question want the potential due to the ring alone?

3. Dec 5, 2007

DieCommie

I assume that r is the distance of an arbitrary point inside the ring to the center. Then a-r would be the distance from the arbitrary point to the ring. Yes, I think it wants potential due to the ring alone.