(Solution) - A thin uniform ring of mass m and radius R is attached by a -(2025 Original AI-Free Solution)

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