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A cylinder of mass M = 2 kg and radius R = 12 cm lies on a plank of the same mass as shown in the figure. The surface between plank and ground is smooth but there is friction between cylinder and plank. If the coefficient of friction between the cylinder and the plank is μ = 0 . 4 , then what maximum initial compression (in cm ) can be given to the spring such that the cylinder moves without slipping with respect to

Options

  1. A2 π m 3 k
  2. B4 π 2 M 3 K
  3. C4 π M 3 k
  4. Dπ 3 M 2 K

Correct answer

C. 4 π M 3 k

Step-by-step solution

Using no Slipping condition: a c + αR = a p f M + 2 f R M R 2 R = k x - f M ⇒ 4 f = k x x max = 4 μMg k ⇒ x max = 4 × 0 . 4 × 2 × 10 200 = 0 . 16   m = 16   cm

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