The potential energy of a particle of mass m is given by `U=(1)/(2)kx^(2)` for `x lt 0` and U = 0 for `x ge 0`. If total mechanical energy of the particle is E. Then its speed at `x = sqrt((2E)/(k))` is

Options

A. (a) Zero
B. (b) `sqrt((2E)/(m))`
C. (c) `sqrt(E/m)`
D. (d) `sqrt((3E)/(2m))`

Answer

A

Explanation

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