A particle free to move along x axis has potential energy g…

Physics Work, Energy, Power and Collision Mix MCQ (Single Correct)

A particle free to move along x axis has potential energy given as U (x) = k (1 - exp (-x 2 )] for - a ≤ x ≤ + ∞ ∞ where k is a positive constant of appropriate dimensions. Then

At points away from the origin, the particle is in unstable equilibrium.

For any finite non-zero value of x, there is a force directed away from the origin.

If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.

If its total mechanical energy is k/2, it has its maximum value at origin.

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The correct answer is:

The graph of U(x) with x is as shown in figure Potential energy is zero at x = 0 and maximum at As mechanical energy has fixed value i.e., k/2, the kinetic energy has to be maximum at x = 0 and maximum at x = ± ± α α .

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