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Suppose that a mass $m$ is suspended from a wire whose length now is $L$. When we remove the mass, the length of the qire becomes $L'$. In this condition how will be the young's modulus of the wire be derived?

We are used to seeing a wire is being stretched by some elongation $l$ and our young's modulus used to be $\frac{FL}{Al}$. But in this case we are in doubt as to what will be the strain since the length is being reduced this time and the force $F$ also disappears suddenly. Will it be $\frac{FL}{A(L-L')}$ in our problem?

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Young’s modulus is experimentally determined here as $\frac{FL'}{A(L-L')}$, as this makes the definition conveniently symmetric for loading and unloading. Of course, one could use $\frac{FL}{A(L-L')}$ with minimal error, as Young’s modulus in this context is defined under a framework of linear (infinitesimal-strain) elasticity; thus, $L\approx L'$.

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