A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

• When a vertical circle is present, the force acting on the particles is greatest when it is acting in the direction of the string's tension force.
• When this situation occurs,
• where $\theta$ is the angle with the lower vertical.
• when $\theta$ is zero cos$\theta$ is maximum and velocity is also maximum 
• when the body is at the lowest position tension is maximum

Hence the correct answer is When the mass is at the lowest point.