A hollow cylindrical pipe of mass M and radius R has a thin rod of mass m welded inside it, along its length. A light thread is tightly wound on the surface of the pipe. A mass `m_(0)` is attached to the end of the thread as shown in figure. The system stays in equilibrium when the cylinder is placed such that `alpha = 30^(@)` The pulley shown in figure is a disc of mass `(M)/(2)`
(a) Find the direction and magnitude of friction force acting on the cylinder.
(b) Express mass of the rod ‘m’ in terms of `m_(0)`

Answer

(a) `f = m_(0)g` towards left
(b) `m = 4 m_(0)`