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The potential energy of a particle of ma...

The potential energy of a particle of mass `m` free to move along the x-axis is given by `U=(1//2)kx^2` for `xlt0` and `U=0` for `xge0` (x denotes the x-coordinate of the particle and k is a positive constant). If the total mechanical energy of the particle is E, then its speed at `x=-sqrt(2E//k)` is

A

zero

B

`sqrt((2E)/(m))`

C

`sqrt(E)/(m)`

D

`sqrt((E)/(2m))`

Text Solution

Verified by Experts

The correct Answer is:
A
From conservation of energy
`KE+PE=E`
or `KE=E-(1)/(2)kx^2`
KE at `x=-sqrt((2E)/(k))` is
`E-(1)/(2)k((2E)/(k))=0`
The speed of particle at `x=-sqrt((2E)/(k))` is zero.
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