The wires $A$ and $B$ shown in the Fig., are made of the same material and have radii $r_A$ and $r_B$ respectively. A block of mass $m$ is connected between them. When a force $F$is $mg/3$, one of the wires breaks.

                   $FA = mg + \frac{mg}{3} = \frac{4mg}{3}$

and       $F_B = \frac{mg}{3}$

             $f_A = \frac{F_A}{\pi {r_A}^2} = \frac{4mg/3}{\pi {r_A}^2}$

and     $f_B = \frac{F_B}{\pi {r_B}^2} = \frac{mg/3}{\pi {r_B}^2}$

For $r_A = 2r_B \Rightarrow f_A=f_B =f$  so either of them break.

For $r_A < 2r_B : f_A>f_B$ $A$ will break before $B$.

For $r_A = r_B \Rightarrow f_A>f$ so $A$ will break before $B$.