First we find the position of center of gravity for the semi-circular ring ABC.
Perimeter of semicircular ring is (πR+2R). Since mass is distributed uniformly, center of gravity will divide the whole lengeth equally and it is located such that
the curved length of the ring is R[(π/2)+1] as shown in figure. Hence the angle subtended by the chord PQ at center is approximately 90º ( arc / radius = angle)..
Hence PG = R/√2 and the force due to gravity (mg) acts at P to give a torque T = (mgR) / √2 .