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 x 2 = 4ay. The wire frame is fixed and the bead can slide on it

Question

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 :

TestHub · Accepted Answer

x 2 = 4ay Differentiating w.r.t. y, we get dy dx = x 2 a It can be considered as an inclined plane ∴ At 2 a, a , dy dx = 1 ⇒ hence θ = 4 5 ∘ the component of weight along tangential direction is mg sin θ . hence tangential acceleration is g sin θ = g 2

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JEE Main 2027 (Class 12+)