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Question

A mass m is attached to a string of length l0, Young's modulus Y and area of cross section A. It is pushed with a velocity v as shown. Find the time in which the block comes to an instantaneous rest.


A
l0v+π2ml02YA
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B
l0v+π2ml04YA
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C
l02v+2π2ml0YA
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D
l0v+2π2ml0YA
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Solution

The correct option is B l0v+π2ml04YA
The string, which is elastic in nature can be replaced by a spring of constant K=YAl0
Thus


i and f are the extreme positions, which the block travels in a time
T4=π2mk
=π2ml0YA
Thus, the total time taken to reach position of instantaneous rest is
t=l0v+π2ml04YA
where l0v: time for string to become taut.

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