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A thin wire is bent into the shape of a parabola in the vertical plane as shown. A small bead ‘P’ can freely slide along the wire. The coefficient of friction between the bead and the wire is 'μ'. The condition on y so that the bead does not slip on the wire is :

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a

y≥2aμ

b

y≥2aμ

c

y≤2aμ

d

y≤2aμ

answer is B.

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Detailed Solution

GivenCoefficient of friction= μFrom diagram y2=4axDifferentiating on both sides 2ydydx=4a ⇒dydx=2ayFor bead to be stationary, slope of tangent on the curve dydx=tanθ≤μ⇒2ay≤μ⇒y≥2aμ

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A thin wire is bent into the shape of a parabola in the vertical plane as shown. A small bead ‘P’ can freely slide along the wire. The coefficient of friction between the bead and the wire is 'μ'. The condition on y so that the bead does not slip on the wire is :