If you put a ball on a string that is 2 meters long and swing it above your head. what distancedoes the ball travel with each circle?

As per the question the length of the string is given as 2 metre.

A  ball is attached to the string.

The ball is taken above the head and the ball starts swinging.

Swinging motion of a body may be oscillatory or circular. Here the motion is circular.

Here the length of the string will be considered as the radius of the circular path. we are asked to calculate the distance traveled by the ball in each  circular rotation.

As the motion is circular, the path covered by the ball in each rotation will be equal to the circumference of the circle.

The circumference of the circle is given as

where C  is the circumference.

                           hence C=2×3.14×2 metre

                                          =.12.56 metre.

Hence distance covered by the ball in each circular rotation is 12.56 metre.

Here the displacement is zero. one should not be confused between distance and displacement.

the answer would be 32*f