Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

\(\Delta L=\frac{F L}{A Y}\)
Because, wires of the same material are stretched by the same load. So, \(F\) and \(Y\) will be constant.
\(
\begin{aligned}
\Delta L & \propto \frac{L}{\pi r^{2}} \\
\Delta L_{1} &=\frac{100}{\pi \times\left(1 \times 10^{-3}\right)^{2}} \\
&=\frac{100}{\pi \times 10^{-6}}=\frac{100}{\pi} \times 10^{-6} \\
\Delta L_{2} &=\frac{200}{\pi \times\left(3 \times 10^{-3}\right)^{2}} \\
&=\frac{200}{\pi \times 9 \times 10^{-6}}=\frac{22.2}{\pi} \times 10^{6} \\
\Delta L_{3} &=\frac{300}{\pi \times\left(3 \times 10^{-3}\right)^{2}} \\
&=\frac{300}{\pi \times 9 \times 10^{-6}}=\frac{33.3}{\pi} \times 10^{6} \\
\Delta L_{4} &=\frac{400}{\pi \times\left(4 \times 10^{-3}\right)^{2}} \\
&=\frac{400}{\pi \times 16 \times 10^{-6}}=\frac{25}{\pi} \times 10^{6}
\end{aligned}
\)
We can see that, \(L=100 \mathrm{~cm}\) and \(r=1 \mathrm{~mm}\) will elongate most.