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Q.

Two masses A and B are connected by a spring.A has mass M,B a mass 2M, and the spring has a negligible mass. The spring is compressed so that the potential energy stored in it is V0 . The system is placed on a horizontal frictionless table and is given a velocity uk^ in the z-direction as shown, and the spring is released. In the subsequent motion the line from B to A always points along thei^ unit vector. The initial total mechanical Energy

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a

In terms of the given quantities E=V0+32Mu2

b

Potential energy is stored in the spring when A and B have kinetic energy KA and KB is P.E=E-KA-KB

c

At some instant of time B is at point p and has a component of velocity in the x–direction of vxi^ . At that instant of time , in terms of the given quantities, the velocity vector vA of  A is vA=-2vxi^+ uk^

d

In subsequent motion A and B undergo circular motion about centre of mass.

answer is A, B, C.

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Detailed Solution

E=v0+12 2Mu2+Mu2\

Energy remains conserved.

E=U+kA+kB

Conserving linear momentum for x-motion.

VA=-2vxI^+uk^

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