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Q.

Two particles (A and B) of masses m and 2m are  joined by a light rigid rod of length L. The system  lies on a smooth horizontal table. The particle  (A) of mass m is given a sharp impulse so that  it acquires a velocity u perpendicular to the rod. Calculate maximum speed of particle B during subsequent motion. 

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a

4u3

b

u

c

u3

d

2u3

answer is C.

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Detailed Solution

Vcm=mu3m=u3
In COM frame, the system rotates with speed of A=2u3 and speed of B=u3
 

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The two figures show the velocities of A and B in COM frame. 
In ground frame B will have maximum velocity when it is in position indicated in fig (b)
VBmax=2u3

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