To determine when the wire is most likely to break, we need to analyze the forces acting on the mass $m$ at different points in the vertical circle.$\\$When the mass is at the lowest point of the circle, the tension in the wire is at its maximum.$\\$Let's analyze the forces at the lowest point:$\\$• The gravitational force acting downward is $mg. \\$• The centripetal force required to keep the mass moving in a circle is $\frac{mv^2}{r},$