Which of the following statements is incorrect? a) Displacement is independent of the choice of origin of the axis. b) Displacement may or may not be equal to the distance travelled. c) When a particle returns to its starting point, its displacement is not zero. d) Displacement does not tell the nature of the actual motion of a particle between the points.

Options

A. Displacement is independent of the choice of origin of the axis.
B. Displacement may or may not be equal to the distance travelled.
C. When a particle returns to its starting point, its displacement is not zero.
D. Displacement does not tell the nature of the actual motion of a particle between the points.

Explanation

To determine which of the given statements about displacement and distance is incorrect, let's analyze each statement step by step.

### Step 1: Understand the definitions
- **Distance** is defined as the actual length of the path covered by a particle. It is a scalar quantity and is always positive.
- **Displacement** is defined as the shortest distance between the initial and final positions of a particle. It is a vector quantity and can be positive, negative, or zero.

### Step 2: Analyze each statement
1. **Statement a**: "Displacement is independent of the choice of origin of the axis."
- This statement is **correct**. Displacement depends only on the initial and final positions, not on where we define the origin.

2. **Statement b**: "Displacement may or may not be equal to the distance travelled."
- This statement is **correct**. Displacement can be equal to the distance travelled if the path is straight. However, if the path is not straight (like in a circular motion), the distance travelled can be greater than the displacement.

3. **Statement c**: "When a particle returns to its starting point, its displacement is not zero."
- This statement is **incorrect**. If a particle returns to its starting point, the initial and final positions are the same, which means the displacement is zero.

4. **Statement d**: "Displacement does not tell the nature of the actual motion of a particle between the points."
- This statement is **correct**. Displacement only provides the shortest distance between two points and does not indicate the path taken.

### Conclusion
The incorrect statement among the options is **Statement c**: "When a particle returns to its starting point, its displacement is not zero."

### Final Answer
The answer is **Option C**.

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