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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
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Asked by vishal.vini86 | 22 Apr, 2022, 12:06: AM
answered-by-expert Expert Answer
( 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  begin mathsize 14px style v square root of m over k end root end style
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
 
begin mathsize 14px style d x space equals space v space square root of fraction numerator m over denominator 2 space k end fraction end root space end style
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(D) Maximum compression is  begin mathsize 14px style v square root of fraction numerator m over denominator 2 k end fraction end root end style
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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