A block of mass m is placed on a smooth wedge of mass M and inclination angle θ. What horizontal force F must be applied to the wedge so that the block remains stationary relative to the wedge?

Answer and explanation

Correct answer: D. (M + m) g tan θ

  1. Step 1: For the block to remain stationary on the wedge, the normal force N cos θ = mg and N sin θ = m a.
  2. Step 2: Dividing gives: tan θ = a / g => a = g tan θ.
  3. Step 3: Total system mass = M + m.
  4. Step 4: Horizontal force required F = (M + m) a = (M + m) g tan θ.

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