Which one of the following is a dimensional constant?

Options

A. refractive index
B. dielectric constant
C. relative density
D. gravitatioanl constant

Answer

To determine which of the given options is a dimensional constant, we need to analyze each option based on whether it has dimensions or is dimensionless.

### Step-by-Step Solution:

1. **Understanding Dimensional Constants**:
A dimensional constant is a physical quantity that has dimensions and is not dimensionless. It typically has units associated with it.

2. **Analyzing the Options**:
- **Refractive Index**:
The refractive index is defined as the ratio of the speed of light in vacuum to the speed of light in a medium. Since it is a ratio of two speeds, it is dimensionless. Therefore, it is not a dimensional constant.

- **Dielectric Constant**:
The dielectric constant (also known as the relative permittivity) is defined as the ratio of the permittivity of a substance to the permittivity of free space. This is also a ratio and hence dimensionless. Thus, it is not a dimensional constant.

- **Relative Density**:
Relative density (or specific gravity) is the ratio of the density of a substance to the density of water. Since this is a ratio, it is dimensionless as well. Therefore, it is not a dimensional constant.

- **Gravitational Constant (G)**:
The gravitational constant is a fundamental physical constant used in the calculation of gravitational effects. It has dimensions, specifically [G] = m³ kg⁻¹ s⁻². Therefore, it is a dimensional constant.

3. **Conclusion**:
Based on the analysis above, the only option that qualifies as a dimensional constant is the **Gravitational Constant (G)**.

### Final Answer:
The dimensional constant among the options is **Gravitational Constant (G)**.

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