Determining which physical quantities definitively "have no SI unit" requires careful consideration. The provided reference states that "velocity, force, momentum, and magnetic field" do not come under SI units, which is inaccurate. These quantities do have SI units, derived from the base SI units. A more accurate question to address based on common misunderstandings is: Which dimensionless quantity is often encountered but technically has no dedicated SI unit?
While it's more precise to say derived SI units can represent velocity, force, momentum, and magnetic field, the original question can be interpreted to mean "which fundamental or dimensionless quantity has no assigned SI unit". With this interpretation, the question becomes more focused. Therefore, instead of quantities with SI units, we look for dimensionless quantities.
Dimensionless Quantities and SI Units
Many physical quantities are dimensionless, meaning they have no physical dimension (e.g., length, mass, time). They are often ratios of quantities with the same dimension, resulting in a pure number. While these quantities exist, the original question can only be answered by reinterpreting to search for dimensionless quantities.
Here's a breakdown:
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Dimensionless Quantities: These are quantities that do not have physical units. Examples include:
- Refractive index: The ratio of the speed of light in a vacuum to the speed of light in a medium.
- Strain: Change in length divided by original length.
- Efficiency: Ratio of output energy to input energy.
- Relative Density Ratio of the density of a substance to the density of a reference substance
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Radians and Steradians: While technically dimensionless, radians (for angles) and steradians (for solid angles) are often treated as having units to aid in clarity and dimensional analysis. They are defined in relation to geometric properties, linking them to length. Radians are the ratio of arc length to radius and Steradians the ratio of area to radius squared, but these are definitions not dimensions.
Conclusion
The question is complex because most physical quantities have derived SI units, even if those units are combinations of base SI units. The most likely intended answer would be a dimensionless quantity, such as refractive index or efficiency which are pure numbers and thus have no dedicated SI unit, though contexts exist where "1" may be considered its unit.
