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Two blocks A and B, each of mass m, are connected by a massless spring of natural length L and spring constant K.
The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in fig.. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elastically with A. Then
  • a)
    the kinetic energy of the A-B system, at maximum compression of the spring, is zero.
  • b)
    the kinetic energy of the A-B system, at maximum compression of the spring, is mv2/4.
  • c)
    the maximum compression of the spring is
  • d)
    the maximum compression of the spring is 
Correct answer is option 'B,D'. Can you explain this answer?
Verified Answer
Two blocks A and B, each of mass m, are connected by a massless spring...
In situation 1, mass C is moving towards right with velocity v. A and B are at rest.
In situation 2, which is just after the collision of C with A, C stop and A acquires a velocity v. [head-on elastic collision between identical masses]
When A starts moving towards right, the spring suffer a compression due to which B also starts moving towards right. The compression of the spring continues till there is relative velocity between A  and B. When this relative velocity becomes zero, both A and B move with the same velocity v' and the spring is in a state of maximum compression.
Applying momentum conservation in situation 1 and 3,



∴ K.E. of the system in situation 3 is
This is the kinetic energy possessed by A – B system (since, C is at rest).
Let x be the maximum compression of the spring.
Applying energy conservation
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Two blocks A and B, each of mass m, are connected by a massless spring of natural length L and spring constant K.The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in fig.. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elastically with A. Thena)the kinetic energy of the A-B system, at maximum compression of the spring, is zero.b)the kinetic energy of the A-B system, at maximum compression of the spring, is mv2/4.c)the maximum compression of the spring is d)the maximum compression of the spring isCorrect answer is option 'B,D'. Can you explain this answer?
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