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Gravitational potential and equilibrium of a thin ring

  1. Dec 4, 2007 #1
    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!!
  2. jcsd
  3. Dec 5, 2007 #2


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    Some clarifications seem to be in order: What is r? Does the question want the potential due to the ring alone?
  4. Dec 5, 2007 #3
    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.
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