Since the centripetal force always points along a raduis toward the center of the od the circle, and the velocity of the object is always tangent to the circle (and thus perpendicular to the radius), the work done by the centripetal force is zero. Alternatively, since the object\textquotesingle s speed remains constant, the Work-Energy Theorem tells you that no work is being performed. 
An object of mass m is traveling at constant speed v in acircular path of radius r. How much work is done by the centripetal force during one-half of a revolution? 
(a) $\pi mv^{2}$ 
(b) $$0$$ 
(c) $\pi mv^{2}r$ 
(d) $2\pi mv^{2}r$ 