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Q.

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 may not be:

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a

μα

b

μα

c

1μα

d

infinitesimal

answer is B, C, D.

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Detailed Solution

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Tangential Force (Ft ) of the bead will be given by Normal reaction (N) while centripetal force (FC ) is provided by friction (f). The bead starts sliding when the centripetal force is just equal to limiting friction

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Ft is inwards

Ft=ma=mαL=N

Limiting value of friction  frmax=μN=μmαL  

Angular velocity at time ‘t’ is ω=αt  

Centripetal Force at time ‘t’ will be Fc=mLω2=mLα2t2  t=μα

For t>μα,FC>frmax  the bead starts sliding

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