A

To solve this problem, we need to first understand the forces acting on a particle in a vertical circular motion.
Step 1: At the highest point of the vertical circle, the gravitational force acting downwards must be sufficient to provide the necessary centripetal force required to keep the particle in circular motion.
Step 2: The forces acting on the particle at the highest point are: the weight of the particle (mg, acting downwards) and the tension (T) in the string (also acting downwards).
Step 3: The net centripetal force required to keep the particle moving in circular motion is provided by the sum of the tension T and the weight mg. Since we are looking for the condition where the tension is zero, we have:
$$ m g = \frac{m v^2}{r} $$
or
$$ v^2 = g r $$
Step 4: This means that at the highest point, if the speed is such that the tension is zero, the particle can still complete the circular motion by just relying on the gravitational force to provide the necessary centripetal force.
Thus, at the highest point, the tension in the string is zero when the particle is just able to complete the vertical circle.
Therefore, the correct answer is option A.