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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 m, and gravity is neglected, then the  time after which the bead starts slipping is



Solution

The correct option is C


Let the bead starts slipping after time t

For critical condition

Frictional force provides the centripetal force

m ω2 L = μ R = μ m × at = μLma

 m(at)2 L = μmLa   t = μa           (As ω = at)

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