Which one of the following statements for the work done by gravity...

The gravitational force is a conservative force.

For any conservative force, the work done is independent of the path taken and depends only on the initial and final positions of the body.

Specifically for gravity, the work done is given by $W = mgh$, where $h$ is the vertical displacement. Thus, it depends only on the vertical distance separating the initial and final positions.

If the displacement is purely horizontal, the angle between the gravitational force (downwards) and the displacement is $90^{{}^{\circ}}$. The work done is $W = Fd \cos(90^{{}^{\circ}}) = 0$.

Therefore, the statement that work done depends on the path followed by the body is incorrect.

Answer: Work done depends on the path followed by the body