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?
- A.Positive work is done by gravity in moving the object from point A to point B.
- B.Negative work is done by gravity in moving the object from point A to point B.
- C.Gravity must be non-conservative in such a region.
- D.No work is done by gravity in moving the object from point A to point B.
Correct answer
Explanation
The correct answer is D, No work is done by gravity in moving the object from point A to point B. Work done by gravity depends only on the difference in potential between the two points, and here that difference is zero.
Gravity is a conservative force. The work it does on a mass m moving from A to B equals m multiplied by the fall in potential, W = m × (potential at A − potential at B). Because V is the same at A and B, the work is zero whatever path the object takes. The field strength at a point is the rate at which potential changes there, so two points on the same equipotential surface can still have different fields.
A is wrong: positive work needs the potential at B to be lower than at A.
B is wrong: negative work needs the potential at B to be higher than at A.
C is wrong: gravity is always conservative; unequal fields at two points do not change that.
Exam tip: equal potential means zero work by a conservative force, regardless of the path or the field values.
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