Question

Select One Option Correct from the following : A particle free to move along the x-axis has potential energy given by $U (x) = k \bigg [1 - e^{-x^{2} } \bigg ] for -\infty \leq x \leq +\infty$, where k is a positive constant of appropriate dimensions. Then,
(A)at points away from the origin, the particle is in unstable equilibrium.
(B)for any finite non-zero value of x, there is a force directed away from the origin.
(C)if its total mechanical energy is k/2, it has its minimum kinetic energy at origin.
(D)for small displacement from x = 0, the motion is simple harmonic.

Answer 1

d option is correct I think

Answer 2

d option is correct.

hope this answer will help you.