The potential energy of a particle of mass m moving along the x-axis is given by U(x) = (a / x^2) - (b / x), where a and b are positive constants. What is the equilibrium position of the particle?

Answer and explanation

Correct answer: D. x = 2a / b

  1. Step 1: Equilibrium condition: Force F = -dU/dx = 0.
  2. Step 2: dU/dx = d/dx [a x^(-2) - b x^(-1)] = -2a x^(-3) + b x^(-2) = (-2a + b x) / x^3.
  3. Step 3: Set dU/dx = 0: -2a + b x = 0 => x = 2a / b.
  4. Step 4: Since d^2U/dx^2 at this point is positive, x = 2a / b is a stable equilibrium.

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