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………….

Question

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………….

Infinity Learn · Accepted Answer

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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