Q56 / 270 · NDA 2026 (Phase 1) · General Ability
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?
- APositive work is done by gravity in moving the object from point $A$ to point $B$.
- BNegative work is done by gravity in moving the object from point $A$ to point $B$.
- CGravity must be non-conservative in such a region.
- Correct answerDNo work is done by gravity in moving the object from point $A$ to point $B$.
Solution
The work done by the gravitational force on an object of mass $m$ in moving it from point $A$ to point $B$ is given by $W = -\Delta U = -m(V_B - V_A) = m(V_A - V_B)$, where $V_A$ and $V_B$ are the gravitational potentials at points $A$ and $B$ respectively.
It is given that the gravitational potential is the same at points $A$ and $B$, which means $V_A = V_B$.
Substituting this into the work equation, we get $W = m(V_A - V_A) = 0$.
The difference in the gravitational field at the two points does not affect the total work done between these equipotential points, as gravity is a conservative force and work done is independent of the path taken.
Therefore, no work is done by gravity in moving the object from point $A$ to point $B$.
It is given that the gravitational potential is the same at points $A$ and $B$, which means $V_A = V_B$.
Substituting this into the work equation, we get $W = m(V_A - V_A) = 0$.
The difference in the gravitational field at the two points does not affect the total work done between these equipotential points, as gravity is a conservative force and work done is independent of the path taken.
Therefore, no work is done by gravity in moving the object from point $A$ to point $B$.
Hence, the correct answer is option: 'D'.