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Question

Sir i have problem in finding velocity of center and trajectory of center. Is there any shortcut to find velocity of center. 
Joshi sir comment

By rigid body constraints

usinθ=vcosθ v = utanθVelocity of centre of mass =[u(-ˆj)+utanθ(ˆi)]/2Let centre of rod is (x,y) (2x)2+(2y)2=L2 

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