When a sphere moves in a horizontal circular path, the centripetal force (provided by the tension in the string) is continuously directed towards the centre of the circle . At any instant, the displacement of the sphere is tangential to the circular path. Since the radius and the tangent are perpendicular to each other, the angle $\theta$ between the centripetal force vector and the displacement vector is $90^\circ$ . The work done by a force is given by $W = Fd \cos \theta$. Thus, $W = Fd \cos 90^\circ = 0$. Therefore, the work done by the centripetal force over a full circle (or any part of the circle) is always zero.