Dimensionless quantity is

Options

A. Intensity level of sound
B. Magnetic susceptibility
C. Refractive index
D. all the above

Answer

To determine which of the given options is a dimensionless quantity, we can analyze each option based on its definition and units.

### Step-by-Step Solution:

1. **Understanding Dimensionless Quantities**:
- A dimensionless quantity is a quantity that has no physical dimensions and is expressed as a pure number. This means that when the units are analyzed, they cancel out completely.

2. **Analyzing the Options**:
- **Intensity of Sound Level**:
- The intensity of sound level is defined in decibels (dB), which is a logarithmic measure of the ratio of a particular sound intensity to a reference intensity. Since it is a ratio of two intensities (which have the same units), the units cancel out, making it dimensionless.

- **Magnetic Susceptibility**:
- Magnetic susceptibility (χ) is defined as the ratio of the intensity of magnetization (I) to the magnetizing field intensity (H). Mathematically, χ = I/H. Since both I and H have the same units (A/m or T), the units cancel out, making magnetic susceptibility also dimensionless.

- **Refractive Index**:
- The refractive index (n) is defined as the ratio of the speed of light in a vacuum to the speed of light in a medium. It can also be expressed as the ratio of the refractive index of a material to that of air. Since this is a ratio of two speeds (which have the same units), the units cancel out, making the refractive index dimensionless as well.

3. **Conclusion**:
- All three options (Intensity of Sound Level, Magnetic Susceptibility, and Refractive Index) are dimensionless quantities. However, if we need to select one, we can choose any of them based on the context of the question.

### Final Answer:
All of the mentioned quantities (Intensity of Sound Level, Magnetic Susceptibility, and Refractive Index) are dimensionless.

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