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Q.

A solid cylinder of mass m = 5 kg and radius R = 0.4 m is given an initial angular velocity ω0=40rads−1 about a horizontal axis through its centre and gently placed on a plank of mass m = 5 kg. The coefficient of friction between the cylinder and plank is μ=0.2. The plank rests on a smooth horizontal surface. The time after which pure rolling motion of cylinder will start relative to the plank is  (Take g=10ms−2 )

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a

2 sec

b

3 sec

c

4 sec

d

5 sec

answer is A.

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Detailed Solution

τCM=lCMαμmgR=mR22αα=2μgRWhen pure rolling motion startsωR−v=v0ω0−αtR−μgt=μgtω0R−2μgt−μgt=μgtω0R=4μgt⇒t=ω0R4μg=40×0.44×0.2×10=2sec
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