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Q. The stress required to double the length of wire of Young's modulus $Y$ is

J & K CETJ & K CET 2009Mechanical Properties of Solids

Solution:

Let $L$ be the length of a wire.
If the length of a wire is doubled, the longitudinal strain will be
$ \frac{\Delta L }{ L }=\frac{2 L - L }{ L }=\frac{ L }{ L }=1 $
Young's modulus $Y =\frac{\text { Stress }}{\text { Strain }}$
$\therefore Y =$ Stress $(\because$ Strain $=1)$.