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Question

# System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is

A
1943u2 m/s
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B
13u2 m/s
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C
3 u m/s
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D
7 u m/s
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Solution

## The correct option is D √7 u m/sMethod - 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

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