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Two identical blocks A and B, each of mass ‘m’  resting on smooth floor are connected by a light  spring of natural length L and the spring  constant K, with the  spring at its natural length.  A third identical block C (mass m) moving with  a speed v along the line joining A and B collides  with A. The maximum compression in the spring is………….

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a

vm/2k

b

mv2k

c

mv2k

d

mv2k

answer is A.

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Detailed Solution

At the time of maximum compressionboth will move with the same velocity say v1 from conservation of linear momentum   mv=2mv1 v1=v2 and from conservation of energy 12mv2=12mv22×2+12kx2 solving x=vm2k
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Two identical blocks A and B, each of mass ‘m’  resting on smooth floor are connected by a light  spring of natural length L and the spring  constant K, with the  spring at its natural length.  A third identical block C (mass m) moving with  a speed v along the line joining A and B collides  with A. The maximum compression in the spring is………….