A plank is moving with a velocity 4m/s. A disc of radius 1m rolls on it without slipping with an angular velocity of 3rad/s as shown in figure. Then, the velocity of the centre of the disc (Vcm) is
A
4m/s
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B
1m/s
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C
3m/s
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D
7m/s
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Solution
The correct option is D7m/s In pure rolling (rolling without slipping) velocity of contact points (P&Q) will be same.
i.e Velocity of disc at contact point=Velocity of plank ⇒VP=VQ...(i) ∵ Tangential velocity (ωR) and translational velocity at P are in opposite direction. ⇒VP=Vcm−ωR&VQ=4m/s
From Eq (i), Vcm−ωR=4 Vcm=4+(3×1) ∴Vcm=7m/s