A uniform rod of mass M and length L is hinged at its lower end so as to rotate freely in the vertical plane of the fig. There is a small tight fitting the hinged end. A small mass less pin welded to the rod supports the bead. The system is released from the vertical position shown. It was observed that the bead just begins to slide on the rod when the rod becomes horizontal.
(a) Find the normal contact force between the rod and the bead when the rod gets horizontal. What is the direction of this force?
(b) Find the coefficient of friction between the bead and rod.

Answer

(a) `(2Mg)/(123)` Vertically down
(b) `mu = 22.5`