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 ]
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2
Drawing free body diagram of the cylinder with respect to plank.
Acceleration of point of contact with respect to plank is 
Velocity of pure rolling starts,
Distance traveled by cylinder with respect to plank in 1s is
At t = 1s , the velocity of cylinder with respect to plank is
t=1s
= -20 + 2 x 0.5 x 10 = -10 m/s
Remaining 10m will be travelled in time 
Total time = 2
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