A thin, uniform ring of mass m and radius R is attached by a frictionless pin to a collar at A and rests against a small roller at B. The ring lies in a vertical plane, and the collar can move freely on a horizontal rod and is acted upon by a horizontal force P.

(a) Express the angle θ corresponding to equilibrium in terms of m and P.

(b) Determine the value of θ corresponding to equilibrium when m = 500 g and P = 5 N.