For an object in gravitational field, the gravitational potential is the same at two points A and B, but the gravitational field is not the same at these two points. Which one of the following statements is correct?

The work done by a conservative force such as gravity depends only on the difference in potential between the initial and final points: W = -(U_B - U_A) = -m(V_B - V_A). Since the gravitational potential at A and B is the same (V_A = V_B), the work done by gravity in moving an object from A to B is zero, regardless of the path taken or the value of the gravitational field at those points. The gravitational field being different at A and B does not violate conservativeness — field is the gradient of potential, and equal potential at two points only means the line integral between them vanishes.