Question

A particle free to move along x axis has potential energy given as U_(x) = k (1 - exp (-x²)] for - a ≤ x ≤ + ∞where k is a positive constant of appropriate dimensions. Then

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

Answer 1

Answer: (D)

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

Answer 2

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.