JEE Class main Answered
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
![question image](https://images.topperlearning.com/topper/new-ate/topr_141125173260271438Capture.jpeg)
Asked by vishal.vini86 | 22 Apr, 2022, 00:06: 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 ![begin mathsize 14px style v square root of m over k end root end style](https://images.topperlearning.com/topper/tinymce/cache/e36f507883a075bf03b223734fae675a.png)
![begin mathsize 14px style v square root of m over k end root end style](https://images.topperlearning.com/topper/tinymce/cache/e36f507883a075bf03b223734fae675a.png)
Above statement is false and explanation is given below
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/ad54dd3e9970d10873d7a3bc0bce3f6b62622738737846.00990823f2.png)
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](https://images.topperlearning.com/topper/tinymce/cache/e9bfc65b88609e7c1d2a84b534031dd8.png)
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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](https://images.topperlearning.com/topper/tinymce/cache/d2d596f2dc8e50a2bf81c4811ee52d2b.png)
![begin mathsize 14px style v square root of fraction numerator m over denominator 2 k end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/d2d596f2dc8e50a2bf81c4811ee52d2b.png)
Above statement is true and explanation is as given in part (C)
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