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A block of mass m = 2 kg is placed on a plank of mass M = 10 kg , which is placed on a smooth horizontal plane, as shown in the figure. The coefficient of friction between the block and the plank is μ = 1 3 . If a horizontal force F is applied on the plank, then the maximum value of F for which the block and the plank move together is g = 10 m / s 2

Options

  1. A50 N
  2. B40 N
  3. C120   N
  4. D100   N

Correct answer

B. 40 N

Step-by-step solution

a = F M + m assuming no slipping between   m and M This means friction between the block and plank is f = m a = m F m + M f = m F m + M ≤ μ m g ⇒ F ≤ M + m g 3 ⇒ F ≤ 40   N

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