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 equations is `x^(2) = 4 ay` . 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 :

Options

A. `(g)/(2)`
B. `(sqrt3g)(2)`
C. `(g)/(sqrt2)`
D. g

Answer

C

Explanation

`x^(2) = 4 ay , (dy)/(dx) = (1)/(2a)x`
at point (2a , 2a) , `(dy)/(dx) = 1 , theta = 45^(@)`
Component of weight along tangetial direction is mg sin `theta`.
Tangential acceleration `(dv)/(dt) = omega (dr)/(dt`
`omega = 4 pi , (dr)/(dt) = 0.5` , a = `2 pi`
`T - "mg" = "ma" , T = "mg" + "ma"`