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 — C, 'Work done depends on the path followed by the body'. This is the false statement (the question asks which is NOT correct). Gravity is a conservative force, so the work it does depends only on the change in height between the start and end points, W = mgh, and not at all on the route taken. Saying it depends on the path directly contradicts that.
- (a)Work done is independent of the path followed by the body — This is a CORRECT statement, so it is not the answer. Because gravity is conservative, its work is path-independent.
- (b)Work done depends only on the vertical distance separating the initial and the final position of the body — This is a CORRECT statement. Work by gravity is W = mgh, where h is the vertical height change; the horizontal part of the motion contributes nothing.
- (d)Work done is zero if the body is displaced horizontally to the force of gravity — This is a CORRECT statement (here 'horizontally to' means perpendicular to gravity). Work is force times displacement times cos of the angle; at 90° that cosine is zero, so purely horizontal motion does no work against gravity.
Gravity is a conservative force. The work it does on a body moving between two points depends only on the vertical height difference, W = mgh, and is completely independent of the path taken. Moving a body along a horizontal level does no work against gravity because the force and displacement are perpendicular.
Three of the four statements say the same true thing in different words — path-independent, depends only on height, zero for horizontal motion. The odd one out flatly asserts the work 'depends on the path', which is the definition of a NON-conservative force. That contradiction is the whole trap.
- Gravity is a conservative force, so the work it does is independent of the path.
- Work done by gravity is W = mgh, set only by the vertical height change.
- When motion is horizontal (perpendicular to gravity), the work done by gravity is zero.
- Path-dependent work is the hallmark of a non-conservative force such as friction, not gravity.
Only the 'depends on the path' claim is false, so the NOT-correct statement is (c).
- Gravity is conservative — its work never depends on the path, only on the height change.
- Motion perpendicular to a force does zero work (cos 90° = 0).
Work done by gravity is tested as a 'which statement is NOT correct' set, slipping in one path-dependent claim among true path-independent ones.
No directly related past PYQ was found.
- practice — not a real PYQ
A force is said to be conservative if the work it does
- (a)depends on the path taken
- (b)is independent of the path and depends only on the end points
- (c)is always zero
- (d)always increases the kinetic energy
Answer(b) is independent of the path and depends only on the end points — gravity is the standard example.
- practice — not a real PYQ
A box is pushed 5 m along a horizontal floor. The work done by gravity on the box is
- (a)maximum
- (b)equal to mgh
- (c)zero
- (d)negative
Answer(c) zero — gravity acts vertically while the displacement is horizontal, so the angle is 90° and the work is zero.