mass certainly cannot be zero at center of mass
by moment of mass, do you mean moment of inertia?
well if it means moment of inertia, it can only be zero if the axis of rotation passes through center of mass. thats a very specific case
acceleration of center of mass is 0 only for the very specific case if it is at rest
EDIT: acceleration ABOUT the center of mass is zero for all rigid bodies!
in the case of angular acceleration. angular acceleration is 0 only for the very particular case, if the axis of rotation passes through center of mass
for rigid bodies, acceleration about com has to be zero.
answer is C