Out of following four dimensional quantities, which one quantity is to be called a dimensional constant

Options

A. Acceleration due to gravity
B. Surface tension of water
C. Weight of a standard kilogram mass
D. The velocity of light in vacuum

Answer

To determine which of the four dimensional quantities is a dimensional constant, we need to analyze each option based on their characteristics.

### Step-by-Step Solution:

1. **Understanding Dimensional Constants**:
- A dimensional constant is a physical quantity that does not change regardless of the conditions or environment. It has a fixed value and dimensions.

2. **Analyzing the Given Quantities**:
- We have four quantities to consider:
- **Acceleration due to gravity (g)**: This varies depending on location (e.g., altitude, latitude) and is not a constant.
- **Surface tension of water**: This can change with temperature and other factors, so it is not a constant.
- **Weight of a standard kilogram mass**: The weight depends on the gravitational field strength, which varies, hence it is not a constant.
- **Velocity of light in vacuum (c)**: This is a fundamental constant of nature and is always approximately \(3 \times 10^8 \, \text{m/s}\) regardless of the conditions.

3. **Identifying the Dimensional Constant**:
- Among the four quantities, the only one that remains unchanged and has a fixed value is the **velocity of light in vacuum (c)**.

4. **Conclusion**:
- Therefore, the dimensional constant among the given options is the **velocity of light in vacuum**.

### Final Answer:
The quantity that is called a dimensional constant is the **velocity of light in vacuum**.

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