A particle free to move along the (x - axis) hsd potential energy given by `U(x)= k[1 - exp(-x^2)] for -o o le x le + o o`, where (k) is a positive constant of appropriate dimensions. Then.

Options

A. at points away form the origin, the particle is in unstable equilibrium
B. for any finite non-zero value of `x`, there is a force directed away form the origin
C. if its total mechanical enegry is `k//2` it has its minimum kinetic energy at the origin.
D. for small displacements form `x =0`, the motions is `SHM`

Answer

D

Explanation

`U(0) =K [1-e^(-0)] =0` so at `x =0` particle has stable equilibrium `F =- (dU)/(dx) alpha - x` so force is directed towards origin from above equation for small displacements form `x = 0` particle makes `SHM`