A particle which is constant to move along the `x`- axis , is subjected to a force in the same direction which varies with the distance `x` of the particle from the origin as `F(x) = -Kx + ax^(3)` . Hero `K` and `a` are positive constant . For `x ge 0`, the functional from of the potential every `U(x)` of the particle is

Options

A.
B.
C.
D.

Answer

D

Explanation

`F = (-dU)/(dx) rArr dU = - F dx`
`rArr U = - int_(0)^(x) (-kx +ax^(3)) dx = (kx^(2))/(2) - (ax^(2))/(4)`
`:. `We get `U =0` at `x= 0` and `x= sqrt(2k//a)`
So `F = 0` at `x= 0`
i.e. , slope of `U` - x graph is at `x= 0`