A smooth rod is fixed at an angle `alpha` to the horizontal. A small ring of mass m can slide along the rod. A thread carrying a small sphere of mass M is attached to the ring. To keep the system in equilibrium, another thread is attached to the ring which carries a load of mass `m_(0)`at its end (see figure). The thread runs parallel to the rod between the ring and the pulley. All threads and pulley are massless.
(a) Find `m_(0)` so that system is in equilibrium.
(b) Find acceleration of the sphere M immediately after the thread supporting `m_(0)` is cut.

Answer

(a) `(M + m) g "sin"alpha`
(b) `((M+ M) g sin^(2)alpha)/(m + M sin^(2) alpha)`