Statement I : A body moving in a circular path is acted upon by the centripetal force. Statement I : Centripetal force acting on the body is doing work to keep it rotating in the circular path.

Statement I is true because a body moving in a circular path requires a centripetal force to constantly change its direction toward the center of curvature [1]. This force acts as a 'center-seeking' force that maintains the circular trajectory. However, Statement II is false. Work is defined as the product of force and displacement in the direction of the force. In uniform circular motion, the centripetal force is always perpendicular to the object's instantaneous velocity (tangential displacement). Since the angle between the force and the displacement is 90 degrees, the work done by the centripetal force is zero. It changes the direction of the velocity but does not change the speed or kinetic energy of the object, meaning it does no work to keep it rotating.

Sources

1. [1] https://web.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Rotation/Circular.html