Which of the following statement is not true?

Options

A. If displacement of a particle is zero, then distance covered may or may not be zero
B. If the distance covered is zero then the displacement must be zero
C. The numerical value of ratio of displacement to distance is equal to or less than one
D. The numerical value of the ratio of velocity to speed is always less than one

Answer

To solve the question, we need to analyze each of the given statements and determine which one is not true. Let's go through each option step by step.

### Step-by-Step Solution:

1. **Understand the Definitions:**
- **Displacement (d)**: The change in position of an object, which is a vector quantity.
- **Distance (D)**: The total path length covered by an object, which is a scalar quantity.

2. **Evaluate Option 1:**
- **Statement**: If the displacement of a particle is 0, then distance covered may or may not be equal to 0.
- **Analysis**: If a particle returns to its original position, the displacement is 0, but the distance covered can be greater than 0 (e.g., moving in a circle).
- **Conclusion**: This statement is true.

3. **Evaluate Option 2:**
- **Statement**: If the distance covered is zero, then the displacement must be zero.
- **Analysis**: If no distance is covered, the object has not moved, meaning there is no change in position, so displacement is also 0.
- **Conclusion**: This statement is true.

4. **Evaluate Option 3:**
- **Statement**: The numerical value of the ratio of displacement to distance is equal to or less than 1.
- **Analysis**: The ratio \( \frac{d}{D} \) (displacement over distance) can be equal to 1 when the object moves in a straight line without changing direction. Thus, it can be less than or equal to 1.
- **Conclusion**: This statement is true.

5. **Evaluate Option 4:**
- **Statement**: The numerical value of the ratio of velocity to speed is always less than 0.
- **Analysis**: Velocity is given by \( \frac{d}{t} \) and speed by \( \frac{D}{t} \). The ratio \( \frac{v}{s} = \frac{d}{D} \). This ratio can be equal to 1 (when the path is straight) and cannot be less than 0, as both displacement and distance are non-negative.
- **Conclusion**: This statement is not true.

### Final Answer:
The statement that is not true is **Option 4**.

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