Question

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod AB. The rod is set in angular motion about A with a constant angular acceleration α . The coefficient of friction between the lead and the rod is μ . Neglecting gravity, the time at which the lead starts slipping is

(1) Infinitesinally small

(2) \(\sqrt{\frac{μ }{\alpha}}\)

(3) \(\frac{μ }{\sqrt{\alpha}}\)

(4) \(\frac{1}{\sqrt{μ \alpha}}\)

Answer 1

 (2) \(\sqrt{\frac{μ }{\alpha}}\)

The reaction of the rod on the bead provides tangential force F_t and the centripetal force (F_C) is provided by friction f_r . The bead slides when f r equals limiting friction.