A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y=4cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction):

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2gC

22gC

2gCab

answer is C.

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Detailed Solution

For particle to be in equilibrium, mgsinθ = mxω2cosθ⇒tanθ=ω2xgAlso, y=4cx2⇒dydx=8cx=slope at point P=tanθEquating both values of tanθ we get, ω2xg=8cx⇒ω2=8cg⇒ω=8cg=22cg

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