A piece of wire is bent in the shape of a parabola `y = Kx^(2)` (y - axis vorical) with a bead of mass m on it . The beat can side on the wire without friction , it stays the wire is now accleated parallel to the bead , where the bead can stay at rest with repect to the wire from the y - axis is

Options

A. `(a)/(gk)`
B. `(a)/(2gk)`
C. `(2a)/(gk)`
D. `(a)/(4gk)`

Answer

B

Explanation

The force acting on the beat as seen by the olserver in the accelerated frame are `: (a) N ,(b) mg , (c) ma` (psevdo force)
The force `
Let `theta ` is the angle which the tengent at `p` make with the `X- axis` . As the beat is in equalibrixum with respect to the wire , therefor
`N sin theta = ma` and `N cos theta = mg`
`:. ten theta = (a)/(g)` ...(i)
But `y = kx^(2)` , Therefore ,
`(dy)/(dx) = 2kx = ten theta ` ....(ii)
From `(i) `and `(ii)`
`2kx = (a)/(g) rArr x= (a)/(2kg)`