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

Options

A. zero
B. `sqrt((2E)/(m))`
C. `sqrt((E)/(m))`
D. `sqrt((E )/(2m))`

Answer

A

Explanation

From conservation of energy
`K.E + P.E = E`
or `K.E = E - (1)/(2) kx_(2)`
K.E at `x =- sqrt((2E)/(k))` is
`E -(1)/(2)k((2E)/(k))=0`
`:.` The speed of particle at `x = - sqrt((2E)/(k))` is zero.