Which one of the following statements for the work done by gravity on a body is NOT correct ?
- A.Work done is independent of the path followed by the body
- B.Work done depends only on the vertical distance separating the initial and the final position of the body
- C.Work done depends on the path followed by the body
- D.Work done is zero if the body is displaced horizontally to the force of gravity
Correct answer
Explanation
The correct answer is C, Work done depends on the path followed by the body. Gravity is a conservative force, so the work it does never depends on the path.
The work done by gravity on a body of mass m is mgh, where h is the vertical height between the start and the end. Whether the body falls straight down, slides along a slope or follows a winding track, gravity does the same work as long as it drops through the same height. This is what makes gravity conservative, and it is why we can define gravitational potential energy. Around any closed path the total work done by gravity is zero.
A is wrong as a choice: path independence is true for gravity.
B is wrong as a choice: the work does depend only on the vertical separation, W = mgh.
D is wrong as a choice: for horizontal motion the displacement is at right angles to gravity, so W = mgd cos 90° = 0.
Exam tip: conservative forces (gravity, spring, electrostatic) do path-independent work; friction is the classic non-conservative force.
Practice Questions
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