A particle of mass m moves in a circular path of radius r under the action of an attractive central force F = -k / r^2. What is the total mechanical energy of the particle (taking potential energy to be zero at infinity)?

Answer and explanation

Correct answer: C. -k / (2r)

  1. Step 1: Centripetal force: m v^2 / r = k / r^2 => m v^2 = k / r.
  2. Step 2: Kinetic energy K = (1/2) m v^2 = k / (2r).
  3. Step 3: Potential energy U = -∫_∞^r (-k / r^2) dr = -k / r.
  4. Step 4: Total energy E = K + U = k / (2r) - k / r = -k / (2r).

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