The following four wires are made of the same material. Which of these will have the larges extension when the same tension is applied to each? 

We know that       $F=\frac{Y Al}{L}=\frac{Y l\pi r^2}{L}$

or                   $l=\frac{F L}{\pi r^{2}Y}$

Since Y and  F are the same for all wires,$l\propto \frac{L}{r^2} or l\propto \frac{L}{d^2}$.

It is easy to see that $\frac{L}{d^2}$ is the highest for the first wire.