A particle with total mechanical energy, which is small and negative, is under the influence of a one dimensional potential `U(x) = x^(4)//4 – x^(2)//2 J` Where x is in meters. At time `t = 0s`, it is at `x = – 0.5` m. Then at a later time it can be found

Options

A. Anywhere on the x axis
B. Between x = - 1.0m to x = 1.0m
C. Between x = - 1.0m to x = 0.0m
D. Between x = 0.0m to x = 1.0m

Answer

C

Explanation

`U(x) = x^4/4-x^2/4`
`F=-(dU(x))/(dx) =-(x^3-x)`
at `x = -0.5`
`F =- [(-0.5)^3 + 0.5]`
`=-4.875`
`F lt 0` at x = `-1/2`
Thus mechanical energy is small and -ve between `x =- 1.0m` to `x =0.0m.`