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

In the equilibrium
`ma cos theta=mg cos (90-theta)=mg sin theta`
`(a)/(g)=tantheta`….`(i)`
`y=kx^(2)`
`(dy)/(dx)=2kx=tan theta` …..`(ii)`
`2kx=(a)/(g)impliesx=(a)/(2gk)`