Exponential Potential Energy Function!

Classical Mechanics Level 4

A particle free to move along the \(X\)-axis has it's potential energy given by the expression, \(U(x) =k[1-e^{-x^2}]\), for \( -\infty<x<+\infty\), where '\(k\)' is a positive constant with appropriate dimensions, then

(A) At any point away from the origin, the particle would be in the state of unstable equilibrium.

(B) For any finite, non zero value of x, there is a force acting on the particle directed away from the origin.

(C) The origin is point of "Stable Equilibrium".

(D) The origin is point of "Unstable Equilibrium".


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