Here's my first attempt at a solution:
First, I calculated the speed of one ring at the point where the tension would be zero.
3mgr(1-cosΘ ) = (1/2) * (3m) * (v^2).
3m * v^2 = 6mgr(1-cosΘ)
Next, since I wanted the centripetal force, I took the result I got and divided by the radius.
Fc =...