A wire of length L and radius r fixed at one end and a force F applied to the other end produces an extension l . The Extension produced in another wire of the same material of length 2L and radius 2r by a force 2F , is $\mathrm{nl}$. The value of n is 

When strain is small, the ratio of the longitudinal stress to the corresponding longitudinal strain is called the Young's modulus (Y) of the material of the body. 

$\mathrm{Y}=\frac{\text{ stress }}{\text{ strain }}=\frac{\mathrm{F}/\mathrm{A}}{\mathrm{l}/\mathrm{L}}$

Where F is force, A the area, l the change in length and L the original length

r being radius of the wire.

Given, ${\mathrm{r}}_2=2{\mathrm{r}}_1,{\mathrm{L}}_2=2{\mathrm{L}}_1,{\mathrm{F}}_2=2{\mathrm{F}}_1$

Since, Young’s modulus is a property of material, we have $\therefore \frac{{\mathrm{F}}_1{\mathrm{L}}_1}{{\mathrm{\pi r}}_1^2{\mathrm{l}}_2}=\frac{2{\mathrm{F}}_1\times 2{\mathrm{L}}_1}{\mathrm{\pi }{\left(2{\mathrm{r}}_1\right)}^2{\mathrm{l}}_2}$

Hence, extension produced is same as that in the other wire.