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Question

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 an initial velocity of 20 m/s towards right. Find the time (in sec) after which plank and cylinder will separate. (g=10 m/s2)

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Solution


fr=μmg=ma
a=5 m/s2
frR=mR22α
Rα=10 m/s2
Now; t=t sec. when rolling will start [Considering length of planck is sufficient ]
αt+Rαt=ϑ0at
(2a+Rα)t=ϑ0
T=2020=1 sec
Now in 1 sec relative displacement of cylinder
=20×11210×1=15 m
At t= 1 sec rolling will start. Centre of cylinder will move speed 5m/s. Planck will move with speed 15m/s. So extra time taken 10=10t1
t1=1 sec
Total time = 1 + 1
= 2 sec

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