# Two blocks and  each of mass , are connected by a massless spring of natural length  and spring constant . 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 , also of mass , moves on the floor with a speed  along the line joining and  and collides elastically with  Then a) The kinetic energy of the  system, at maximum compression of the spring, is zero b) The kinetic energy of the  system, at maximum compression of the spring, is c) The maximum compression of the spring is d) The maximum compression of the spring is

## Question ID - 100686 | SaraNextGen Top Answer Two blocks and  each of mass , are connected by a massless spring of natural length  and spring constant . 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 , also of mass , moves on the floor with a speed  along the line joining and  and collides elastically with  Then a) The kinetic energy of the  system, at maximum compression of the spring, is zero b) The kinetic energy of the  system, at maximum compression of the spring, is c) The maximum compression of the spring is d) The maximum compression of the spring is

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Answer Key / Explanation : (b,d) -

(b,d)

In situation (i), mass  is moving towards right with velocity .  and  are at rest. In situation (ii), which is just after the collision of  with ,  stops and  acquires a velocity  When  starts moving towards right, the spring suffers a compression due to which  also starts moving towards right. The compression of the spring continues till there is a relative velocity between  and . Once this relative velocity becomes zero, both  and  move with the same velocity  and the spring is in a state of maximum compression

Applying momentum conservation in situations (ii) and (iii),

Therefore, KE of the system in situation (iii) is

Applying energy conservation, we get

Solve to get

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