Tangential force (F1​) of the bead will be given by the normal reaction (N), while centripetal force (Fc​) is provided by friction (fr​). The bead starts sliding when the centripetal force is just equal to the limiting friction.Therefore, Ft​=mat​=mαL=N∴ Limiting value of friction(fr​)max​=μN=μmαL…(i)Angular velocity at time t is ω=αt∴ Centripetal force at time t will beFc​=mLω2=mLα2t2…(ii)Equating Eqs. (i) and (ii), we gett=αμ​​For t>αμ​​,Fc​>(fr​)mux​ i.e. the bead starts sliding.