A particle free to move along the `x-`axis has potential energy given by `U(x) = k[1 - e^(-x^(2))]` for `-oo le x le + oo`, where `k` is a positive constant of appropriate dimensions. Then select the incorrect optionA. 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 originC. If its total mechanical enerfy is `k//2`, it has its minimum kinetic energy at the origin.D. for small displacements from `x = 0`, the motion is simple harmonic.

A particle free to move along the `x-`axis has potential energy given

1.	A particle free to move along the `x-`axis has potential energy given by `U(x) = k[1 - e^(-x^(2))]` for `-oo le x le + oo`, where `k` is a positive constant of appropriate dimensions. Then select the incorrect optionA. 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 originC. If its total mechanical enerfy 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» Correct Answer - A::B::C

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