Consider the following question:
In which of the following situations would a force be exerted on an object and no work be done on the object?
I. a centripetal force is exerted on a moving object
II. a force in the opposite direction as the object is moving
III. a force is exerted on an object that remains at rest
A.) I only
B.) I and II
C.) I and III
D.) II and III
E.) I, II, and III
My response to this question is only II, but this is not a choice. I do not understand how I or III could have work. My logic is that in I, the force is centripetal and therefore is not parallel to the object's path, in any case it would be perpendicular because centripetal is towards the center. Work must be parallel. In III, if an object remains at rest, $d = 0$. And $W = fd$, so $W = 0$.
I can't find the flaw in my logic. Any help is appreciated!