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A particle free to move along X-axis has potential energy given as U(X) =k(1-e⁻ˣ²)

A particle free to move along X-axis has potential energy given as U(X) =k(1-e-ˣ²),where k is a positive constant of appropriate dimension.Then, for -a

Options

(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 isk/2, it has its minimum kinetic energy at the origin
(d) if its total mechanical energy isk/2, it has its maximum kinetic energy at the origin

Correct Answer:

if its total mechanical energy isk/2, it has its maximum kinetic energy at the origin

Explanation:

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