A solid cylinder is kept on one edge of a plank of same mass and length 25 m placed on a smooth surface as shown in the figure. The coefficient of friction between the cylinder and the plank is 0 . 5 . The plank is given a velocity of 20 m s - 1 towards right. Find the time (in s ) after which plank and cylinder will separate. [ g = 10 m s - 2 ]

Step-by-step solution

Drawing free body diagram of the cylinder with respect to plank. 2 μ m g = m a ⇒ a = 2 μ g μ m g R = 1 2 m R 2 α ; α - 2 μ g r Acceleration of point of contact with respect to plank is 4 μ g Velocity of pure rolling starts, - v + 4 μ g t = 0 t = 20 4 × 0.5 × 10 = 1 s Distance traveled by cylinder with respect to plank in 1s is S ′ = - v t + 1 2 2 μ g t 2 = - 15 m At t = 1 s , the velocity of cylinder with respect to plank is t = 1 s v r e l = - v + 2 μ g t = - 20 + 2 × 0.5 × 10 = - 10 m/s Remaining 10 m will