Question

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 ______

Answer 1

Slope $=\frac{\Delta l / w }{ L }=\frac{\Delta l / L }{ w }=\frac{1}{ YA }$
$\Rightarrow Y =\frac{1}{(\text { slope }) A }$
$ Y =\frac{1}{2 \times 10^{-6}\left(0.25 \times 10^{-5}\right)} $
$ Y =2 \times 10^{11} N / m ^2$