A particle moves along the circumference of a circle of radius r when its completes one rotation.

Options

A. Distance travelled is zero and displacement is `2pir`
B. distance and displacement are zero
C. distance is `2pir` but displacement is zero
D. distance and displacement are `2pir` each

Answer

To solve the problem, we need to understand the concepts of distance and displacement in the context of a particle moving along the circumference of a circle.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- A particle moves along the circumference of a circle with radius \( r \).
- It completes one full rotation around the circle.

2. **Calculating Distance**:
- The distance traveled by the particle is the total length of the path it covers.
- The length of the circumference of a circle is given by the formula:
\[ \text{Distance} = 2\pi r \]
- Since the particle completes one full rotation, the distance traveled is \( 2\pi r \).

3. **Calculating Displacement**:
- Displacement is defined as the shortest distance from the initial position to the final position.
- In this case, the particle starts at a point (let's say point A) and after one complete rotation, it returns to the same point (point A).
- Therefore, the initial and final positions are the same, which means:
\[ \text{Displacement} = 0 \]

4. **Final Result**:
- The distance traveled by the particle is \( 2\pi r \).
- The displacement of the particle is \( 0 \).

Thus, the correct answer is:
- Distance = \( 2\pi r \)
- Displacement = \( 0 \)