Gravitational potential and equilibrium of a thin ring

[DieCommie]

Homework Statement

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.)

Homework Equations

The Attempt at a Solution

I drew the picture and tried to figure some sort of integral using law of cosines. I couldn't 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

 

[Gokul43201]

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

 

[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.