Two particles of masses M and m (M gt m) are connected by a light string of length `piR`. The string is hung over a fixed circular frame of radius R.

Initially the particles lie at the ends of the horizontal diameter of the circle (see figure). Neglect friction. (a) If the system is released, and if m remains in contact with the circle, find the speed of the masses when M has descended through a distance `R theta (theta lt pi)`. (b) Find the reaction force between the frame and m at this instant. (c) Prove that m1 will certainly remain in contact with the frame, just after the release, if 3m gt M.

Answer

(a) `sqrt(2gR ((M theta-m sin theta))/(M+m))`
(b) `(mg)/(M+m) [(M+3m) sin theta -2M theta]`