What is the ratio of displacement to the path length traversed by an object, if the object comes back to its initial position?

Explanation

To solve the question, we need to understand the concepts of displacement and path length.

### Step-by-Step Solution:

1. **Define Displacement**: Displacement is defined as the shortest distance from the initial position to the final position of an object, along with the direction. It is a vector quantity.

2. **Initial and Final Position**: In this scenario, the object returns to its initial position. Therefore, the initial and final positions are the same.

3. **Calculate Displacement**: Since the object ends up at the same position where it started, the displacement is:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 \]

4. **Define Path Length**: Path length is the total distance traveled by the object, regardless of the direction. It is a scalar quantity.

5. **Path Length Calculation**: The path length will be a positive value, as it represents the total distance the object has traveled to return to its starting point.

6. **Ratio of Displacement to Path Length**: Now, we can find the ratio of displacement to path length:
\[ \text{Ratio} = \frac{\text{Displacement}}{\text{Path Length}} = \frac{0}{\text{Path Length}} = 0 \]

### Conclusion:
The ratio of displacement to the path length traversed by an object, if the object comes back to its initial position, is **0**.