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Two block 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, moving on the floor with a speed v along the line joining A and B, and collides elastically with A. Then
Asked by vishal.vini86 | 22 Apr, 2022, 12:06: AM
( A ) Kinetic energy of A-B system , at maximum compression of spring is zero

Above statement is true becuase all the kinetic energy of A-B system is converted to get maximum
potential energy at maximum compression of spring .

Hence , when the spring is at maximum compression , kinetic energy of A-B system is zero.
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(B) Kinetic energy of A-B system at maximum compression of spring is  [ (1/4) m v2 }

Above statement is false as per the explanation given in part (A)

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(C) Maximum compression is
Above statement is false and explanation is given below

As shown in figure , when the spring is compressed , equal decrease of length dx occurs at both ends .

hence distance of compression is ( 2 dx )

if distance of compression is maximum, then

(1/2) k ( 2 dx )2 = (1/2) m v2

where k is spring constant , m is mass of block that compress the spring by its maximum speed v

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(D) Maximum compression is
Above statement is true and explanation is as given in part (C)

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Answered by Thiyagarajan K | 22 Apr, 2022, 09:34: AM
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