We know,

\(\text { Stress }=\frac{\text { Force }}{\text { Area }}\)

So, Stress \(\times\) Area \(=\) Force

\(S \times A=F\)

\(\left\{\begin{array}{l}S=\text { Stress } \\ F=\text { Force } \\ A=\text { Area } \\ r=\text { radius }\end{array}\right\}\)

\(\because\) (Since) Force applied on the wires is equal we can relate two conditions as

\(S_1 A_1=S_2 A_2\)

\(\frac{S_1}{S_2}=\frac{A_2}{A_1}=\frac{\pi r_2^2}{\pi r_1^2}\)

\(\frac{S_1}{S_2}=\frac{r^2}{(2 r)^2}=\frac{r^2}{4 r^2}=\frac{1}{4}\)

\(\left\{\begin{array}{l}\text { Where } \\ S_1-\text { Stress in } 1^{\text {st }} \text { wire } \\ A_1-\text { Area of } 1^{\text {st }} \text { wire } \\ r_1-\text { Radius of } 1^{\text {st }} \text { wire } \\ S_2-\text { Stress in } 2^{\text {nd }} \text { wire } \\ A_2-\text { Area of } 2^{\text {nd }} \text { wire } \\ r_2-\text { Radius of } 2^{\text {nd }} \text { wire }\end{array}\right\}\)