Explain with the help of an example, if the displacement of a particle is zero, then it is not necessary that the distance traversed by it is also zero.

Explanation

To explain the concept that if the displacement of a particle is zero, it does not necessarily mean that the distance traversed by it is also zero, we can follow these steps:

### Step-by-Step Solution:

1. **Define Displacement and Distance**:
- Displacement is a vector quantity that refers to the change in position of an object. It is defined as the shortest straight line distance from the initial position to the final position, along with the direction.
- Distance, on the other hand, is a scalar quantity that refers to the total length of the path traveled by the object, irrespective of the direction.

2. **Consider a Circular Path**:
- Imagine a particle moving along a circular path. Let's denote the starting point as point A.

3. **Movement of the Particle**:
- The particle starts at point A and moves around the circular path, eventually returning to point A after completing one full revolution.

4. **Calculate Displacement**:
- Since the particle starts and ends at the same point (point A), the initial and final positions are identical. Therefore, the displacement of the particle is:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = A - A = 0 \]

5. **Calculate Distance**:
- The distance traveled by the particle is the total length of the circular path it covered. The circumference of a circle is given by the formula:
\[ \text{Distance} = 2\pi r \]
where \( r \) is the radius of the circular path. Thus, the distance covered by the particle in one complete revolution is \( 2\pi r \), which is clearly not zero.

6. **Conclusion**:
- In this example, we see that while the displacement of the particle is zero (since it returned to its starting point), the distance it traveled is \( 2\pi r \), which is a positive value. This illustrates that it is indeed possible for the displacement to be zero while the distance traversed is not.