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

Options

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

Explanation

To answer the question, "If the displacement of a body is zero, is the distance covered by it necessarily zero?" we can follow a systematic approach:

### Step-by-Step Solution:

1. **Understanding Displacement and Distance**:
- 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.
- Distance, on the other hand, is the total path length traveled by the object, regardless of direction. It is a scalar quantity.

2. **Analyzing the Condition**:
- The question states that the displacement of a body is zero. This means that the initial and final positions of the body are the same.

3. **Illustration with an Example**:
- Consider a scenario where a person walks in a circular path and returns to the starting point.
- Let’s say the person starts at point A, walks around a circular path, and returns to point A.

4. **Calculating Displacement**:
- Since the person starts and ends at the same point (point A), the displacement is:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = A - A = 0 \]

5. **Calculating Distance**:
- While the displacement is zero, we need to calculate the distance traveled. The distance traveled by the person is equal to the circumference of the circle.
- If the radius of the circle is \( R \), the distance covered is:
\[ \text{Distance} = \text{Circumference} = 2\pi R \]

6. **Conclusion**:
- From this example, we see that the displacement is zero (since the initial and final positions are the same), but the distance covered is not zero (it is \( 2\pi R \)).
- Therefore, we conclude that if the displacement of a body is zero, the distance covered by it is not necessarily zero.

### Final Answer:
No, if the displacement of a body is zero, the distance covered by it is not necessarily zero. For example, a person walking around a circular path and returning to the starting point has zero displacement but has covered a non-zero distance.