A pendulum bob of mass m is suspended by a string of length L. What minimum horizontal velocity must be imparted to the bob at its lowest point so that it completes a full vertical circle?

Answer and explanation

Correct answer: A. sqrt(5 g L)

  1. Step 1: At the topmost point, minimum speed requires string tension T ≥ 0: m v_top^2 / L = m g => v_top = sqrt(g L).
  2. Step 2: Conservation of energy between lowest and highest points: (1/2) m u^2 = (1/2) m v_top^2 + m g (2L).
  3. Step 3: u^2 = v_top^2 + 4 g L = g L + 4 g L = 5 g L => u = sqrt(5 g L).

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