A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is
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(b)
$\Delta \ell=\frac{ F ( L / 2)}{ AY }=\frac{( AL \rho g )( L / 2)}{ AY }$
$=\left(\frac{1}{2}\right) \rho g L ^2 / Y$
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