question_answer

A long horizontal rod has a bead which can slide along its length and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration a. If the coefficient of friction between the rod and the bead is u, and gravity is neglected, then the time after which the bead starts slipping is:

A) \[\sqrt{\frac{\mu }{\alpha }}\]    

B)

C) \[\frac{\mu }{\sqrt{\alpha }}\]                

D) infinitesimal

Correct Answer: A

Solution :

Rod AB is set in angular motion about A, hence the radius of circular path of the bead is L. Its tangential acceleration is  and therefore tangential force acting on the bead of mass m is = where a is the angular acceleration of the bead. Normal (or radial) force on the bead   where  is the angular velocity of the bead. The bead just starts slipping over the rod when