A particle free to move along the x-axis has potential energy given by U(x) = K [1-exp(-x)2] for – ∞<–x<–+∞, where k is a positive constant of appropriate dimensions. Then 

(a)  At point 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 the origin

(d)  For small displacements from x = 0, the motion is simple harmonic

Answer: d

(11)