If the displacement of a body is zero is the distance covered by it necessarily zero ? Explain with suitable illustration.

Options

A. Must be zero
B. May or may not be zero
C. Cannot be zero
D. Depends upon the particle

Explanation

To solve the question, "If the displacement of a body is zero, is the distance covered by it necessarily zero?" we can analyze the concepts of displacement and distance step by step.

### Step-by-Step Solution:

1. **Understanding Displacement and Distance**:
- Displacement is defined as the shortest straight-line distance from the initial position to the final position of an object, along with the direction. It can be expressed mathematically as:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \]
- Distance, on the other hand, is the total length of the path traveled by the object, regardless of direction. It is always a non-negative quantity.

2. **Scenario with Zero Displacement**:
- Consider an object that moves in a circular path. Let’s say it starts at point A, moves around the circle, and returns to point A.
- In this case, the initial position and final position are the same (both at point A). Therefore, the displacement is:
\[ \text{Displacement} = A - A = 0 \]

3. **Calculating Distance in the Same Scenario**:
- While the displacement is zero, we can calculate the distance traveled by the object. The distance covered in one complete revolution around the circle is equal to the circumference of the circle.
- The circumference \(C\) of a circle is given by the formula:
\[ C = 2\pi r \]
- Here, \(r\) is the radius of the circle. Thus, the distance traveled by the object is \(2\pi r\), which is a positive value.

4. **Conclusion**:
- From the above analysis, we conclude that even though the displacement is zero (as the object returns to its starting point), the distance covered is not zero. In this case, the distance is \(2\pi r\).
- Therefore, it is not necessary for the distance to be zero when the displacement is zero.

### Final Answer:
No, it is not necessary that the distance covered by a body is zero if its displacement is zero. For example, if an object moves in a circular path and returns to its starting point, its displacement is zero, but the distance covered is equal to the circumference of the circle, which is \(2\pi r\).