Q.

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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a

2gC

b

2gC

c

22gC

d

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=tanθ​Equating both values of tanθ we get, ω2xg=8cx​⇒ω2=8cg​⇒ω=8cg=22cg
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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):