The Young's modulus $\left(E\right)$ is a property of the material that tells us how easily it can stretch and deform and is defined as the ratio of tensile stress $\left(\sigma \right)$ to tensile strain $\left(\epsilon \right)$.

$$\begin{gathered} Y=\frac{{\displaystyle \frac{F}{A}}}{{\displaystyle \frac{\mathrm{d}l}{l}}} \\ \Rightarrow \mathrm{d}l=\frac{l}{\left(\pi d^2\right)}\times \frac{4F}{Y} \end{gathered}$$

As in our case, value of $\frac{4F}{Y}$ will be constant.

Therefore, for maximum elongation, value of $\frac{l}{\left(\pi d^2\right)}$ should be maximum.

Hence, for $l=50 \mathrm{cm}$ and $d=0.5 \mathrm{mm}$ elongation will be maximum.