The following four wires are made of the same material. Which of these will have the largest  elongation when the same tension is applied

$\mathrm{e}=\frac{\mathrm{FL}}{\mathrm{AY}}=\frac{4\mathrm{FL}}{{\mathrm{\pi d}}^2\mathrm{Y}};\mathrm{e}\propto \frac{\mathrm{L}}{{\mathrm{d}}^2}$

$\text{ For wire A: }\frac{\mathrm{L}}{{\mathrm{D}}^2}=\frac{50}{(0.05{)}^2}=20000$

$\text{ For wire }\mathrm{B}:\frac{\mathrm{L}}{{\mathrm{D}}^2}=\frac{100}{(0.1{)}^2}=10000$

$\text{ For wire }\mathrm{C}:\frac{\mathrm{L}}{{\mathrm{D}}^2}=\frac{200}{(0.2{)}^2}=5000$

$\text{ For wire }\mathrm{D}:\frac{\mathrm{L}}{{\mathrm{D}}^2}=\frac{300}{(0.3{)}^2}=3333.33$

So we can say that the wire with length of 50cm and diameter of 0.5mm will have the maximum elongation.