In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ and $5\,m )$ but of same cross section $\left(2\,mm ^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,Nm ^{-2}$, then the value of $x$ is
JEE MAIN 2022, Medium
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Slope $=\frac{\Delta l / W }{ L }=\frac{\Delta l / L }{ w }=\frac{1}{ YA }$
$Y =\frac{1}{\text { (slope) A }}$
$Y =\frac{1}{2 \times 10^{-6}\left(0.25 \times 10^{-5}\right)}$
$Y =2 \times 10^{11} N / m ^{2}$
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