A bullet of mass m moving with speed v strikes a stationary wooden block of mass M suspended by a light vertical cord of length L and gets embedded in it. To what maximum vertical height does the block-bullet system rise?

Answer and explanation

Correct answer: B. [m v / (M + m)]^2 / (2g)

  1. Step 1: Inelastic collision conserves linear momentum: m v = (M + m) V_common.
  2. Step 2: Common velocity V_common = [m / (M + m)] v.
  3. Step 3: Energy conservation during upward swing: (1/2) (M + m) V_common^2 = (M + m) g h.
  4. Step 4: h = V_common^2 / (2g) = [m v / (M + m)]^2 / (2g).

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