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 in vertical plane 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 :

(A) g / 2

(B) 2 / √3g

(C) g / √2

(D) g / √5

Answer 1

Correct option: (C) g / √2

Explanation:

x² = 4ay

Differentiating w.r.t. y, we get

the component of weight along tangential direction is mg sin θ.

hence tangential acceleration is g sin θ =g / √2