In density and buoyancy calculations, what is the unit of relative density (also called specific gravity)?

Introduction / Context:
Relative density, also known as specific gravity, is a useful concept in fluid mechanics and material science. It compares the density of a substance to the density of a reference substance, usually water for liquids and solids, or air for gases. Because it is a ratio of two densities, its unit behaviour is different from absolute density. This question asks you to identify whether relative density has an SI unit.

Given Data / Assumptions:

• Relative density is defined as density of a substance divided by density of a reference substance at a specified temperature.
• Density itself has units of mass per unit volume, for example kg/m3.
• The reference density uses the same units as the substance density.
• We are working in SI units and standard definitions.

Concept / Approach:
Relative density is the ratio of two densities with the same unit. When one quantity with units is divided by another quantity with the same units, the units cancel. The result is a pure number that tells how many times denser a substance is compared with the reference. Therefore, relative density has no units. For example, if a liquid has density 1200 kg/m3 and water has density 1000 kg/m3, the relative density is 1200 / 1000 = 1.2, and this 1.2 is a dimensionless number.

Step-by-Step Solution:
Step 1: Write the definition: relative density = density of substance / density of reference.Step 2: Use symbols: RD = rho_substance / rho_reference.Step 3: Note that both numerators and denominators have the same SI unit, usually kg/m3.Step 4: When dividing kg/m3 by kg/m3, the units cancel completely.Step 5: The result is a pure number with no units attached.Step 6: Therefore, relative density has no unit.

Verification / Alternative check:
Many data tables for specific gravity list values without any units, for example specific gravity of mercury approximately 13.6, specific gravity of gasoline around 0.7, etc. Laboratories measure specific gravity using hydrometers and report dimensionless values. If relative density truly had units such as kg/m3, these would be included in tables and would not cancel. This practical usage confirms that relative density is dimensionless and has no unit.

Why Other Options Are Wrong:
kg/m is the unit of linear mass density, which is mass per unit length, not relevant for volumetric density ratios. kg/m2 is unit of surface mass density, again unrelated. kg/m3 is the unit of absolute density, not of relative density. While density itself is measured in kg/m3, relative density is a ratio of two densities and therefore does not carry this unit.

Common Pitfalls:
A frequent mistake is to assume that because relative density involves density, it must inherit the same units. Another error is to confuse absolute density with relative density and use them interchangeably. To avoid these mistakes, remember that any time you see a ratio of two quantities with the same units, the units cancel, making the ratio dimensionless. Relative density is always a pure number and never carries units.

Final Answer:
Relative density has no unit; it is a dimensionless quantity.