A particle, which is constrained to move along x-axis, is subjected to a force in the some direction which varies with the distance x of the particle from the origin an `F (x) =-kx + ax^(3)`. Here, k and a are positive constants. For `x(ge0,` the functional form of the potential energy (u) U of the U (x) the particle is.
(a) , (b) , (c) , (d) .

Options

A. (a)
B. (b)
C. (c)
D. (d)

Answer

D

Explanation

`dU_((x))=-Fdx`
`:. U_x=underset0oversetx intFdx=(kx^2)/(2)-(ax^4)/(4)`
`U=0` at `x=0` and at `x=sqrt((2k)/(a))`
`U(x)` is negative for `xgtsqrt((2k)/(a))`
`F=0` at `x=0`. It means slope of `U-x` graph is zero at `x=0`.