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A piece of wire is bent in the shape of ...

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

A

`a/(gk)`

B

`a/(2gk)`

C

`(2a)/(gk)`

D

`a/(4gk)`

Text Solution

Verified by Experts

The correct Answer is:
B
For the bead to stay at rest,
`N cos theta=mg, N sin theta=ma`
Which give `tan theta=a/g`, Now
`tan theta=` slope of the curve =
`(dy)/(dx)=d/(dx)(kx^(2))=2kx, 2kx=a/g rArr x=1/(2gk)`
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