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. The rod is set in angular motion about A with a constant angular acceleration, α. If the coefficient of friction between the rod and bead is µ, and gravity is neglected, then the time after which the bead starts slipping is :–
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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. The rod is set in angular motion about A with a constant angular acceleration, α. If the coefficient of friction between the rod and bead is µ, and gravity is neglected, then the time after which the bead starts slipping is :–

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G1 Physics · Accepted Answer

Before slipping, radial friction must supply mω²L and the transverse normal is mαL. The limiting condition is mω²L=µ(mαL), so ω²=µα. Since ω=αt from rest, t=√(µ/α). Hence A.