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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


  1. 1943u2 m/s
  2. 13u2 m/s
  3. 3 u m/s
  4. 7 u m/s


Solution

The correct option is D 7 u m/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=Vycos30Vxcos60
 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(cos60cos30)=3u
and Vx=2u
V=V2x+V2y=7u
 

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