The extension versus load graph for a wire of length 'L' and radius 'r' is a straight line passing through the origin as shown in figure. The slope of this line is tan θ. From this graph, the Young's modulus Y of the material of wire can be calculated using the formula -
1
\(\rm Y=\frac{L}{\pi r^{2} \tan \theta}\)
2
\(\rm Y=\frac{L \tan \theta}{\pi r^{2}}\)
3
\(\mathrm{Y}=\frac{\pi \mathrm{r}^{2} \tan \theta}{\mathrm{~L}}\)
4
\(\mathrm{Y}=\frac{\pi_{\mathrm{L}}}{2 \pi \mathrm{r}} \tan \theta\)