Let's assume the mass of the ball is m and its speed at the bottom of the circle is v. The potential energy of the ball at the top of the circle is mgh, where h is the height of the circle (which is equal to the length of the string), and g is the acceleration due to gravity. The kinetic energy of the ball at the bottom of the circle is (1/2)mv^2.
Therefore, mgh = (1/2)mv^2
Solving for v, we get:
v = sqrt(2gh)
Substituting the given values, we get:
v = sqrt(2 x 9.81 m/s^2 x 0.75 m) ≈ 3.43 m/s
Therefore, the minimum velocity that the ball must have to make it around the circle is approximately 3.43 m/s.