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Q.

A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equation is  x2= 4ay. The wire frame is fixed and the bead can slide on it without friction. The bead is released from the point y= 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y=a is

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a

g2

b

3g2

c

g3

d

g4

answer is A.

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Detailed Solution

x2=4ay ; dydx=12ax at point 2a, 2a, dydx=1 ; θ=45

Component of weight along tangential direction is mg sinθ
Tangential acceleration is g sinθ

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A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equation is  x2= 4ay. The wire frame is fixed and the bead can slide on it without friction. The bead is released from the point y= 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y=a is