System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is
A
√19−4√3u2m/s
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B
√13u2m/s
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C
√3um/s
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D
√7um/s
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Solution
The correct option is D√7um/s Method - I Let the velocity of the cylinder be V, whose x and y components are Vx and Vy respectively. As cylinder will remain in contact with wedge A and B ⇒Vx=2u
And, from the FBDs ucos60∘=Vycos30∘−Vxcos60∘ ⇒ucos60∘+Vxcos60∘=Vycos30∘ ⇒ucos60∘+2ucos60∘=Vycos30∘ ⇒3u(12)=Vy(√32) ⇒Vy=√3u ∴V=√V2x+V2y=√7u
Method - II In the relative frame i.e. frame of A, the arrangement will be as shown in the below figure
3ucos60∘=Vycos30∘ ⇒Vy=3u(cos60∘cos30∘)=√3u and Vx=2u ⇒V=√V2x+V2y=√7u