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 $(2\ \text{mm}^2)$ 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 $x\times10^{11}\ \text{N m}^{-2}$, then the value of $x$ is ______ .
Numerical value type. Enter your answer.
Answer: 2
$\dfrac{\text{extension}}{\text{load}} = \dfrac{L}{YA}$, so the slope of this graph against $L$ is $\dfrac{1}{YA}$.
From the graph, slope $= \dfrac{0.25\times10^{-5}}{1} = 2.5\times10^{-6}\ \text{N}^{-1}$.
$$Y = \frac{1}{A\times\text{slope}} = \frac{1}{2\times10^{-6}\times2.5\times10^{-6}} = 2\times10^{11}\ \text{N m}^{-2}$$
$x = 2$.
Solution by Sreeraj P, M.Sc Physics