A solid cylinder having radius 0.4 m, initially rotating (at t = 0) with ω0 = 54 rad/sec is placed on a rough inclined plane with θ=370 having friction coefficient μ = 0.5. The time taken by the cylinder to start pure rolling is:
A
5.4 sec
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B
1.4 sec
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C
1.2 sec
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D
1.8 sec
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Solution
The correct option is D 1.2 sec At the instant when the cylinder sides friction (f) will be maximum ⇒f=μN=(0.5)×45mg=25mg(N=Nomal Force )
FBD of cylindur weget - f+35mg=ma⇒25mg+35mg=ma⇒[a=g] From law of molion v=u+at(u=0 initial linear velocity )⇒v=gt−1 - From Rotational motion ω=ω0+αtα= angular accelesation From torque equation τ=fR=25mgR=Iα
⇒−25mgR=mR22α⇒α=−4g5R we get →ω=ω0−4g5Rtω=54−4gt5R=VR−(2)
The pure Rolling will stact when v=Rw⇒ From eq D and 2gtR=544gt5Rt=54×5R9g=54×5×0.49×10t=1.2 sec Hence, option (C) is correct.