What is the S.I unit of relative density?

1. Analyze the question

The question asks for the S.I. unit of relative density. To answer this, we need to understand what relative density represents physically and how it is calculated.

2. Explain the concept

Relative density (also known as specific gravity) is defined as the ratio of the density of a substance to the density of a standard substance (usually water at 4°C).

The formula is:

Since density is measured in $\text{kg/m}^3$ (or $\text{g/cm}^3$), the calculation looks like this:

Because the units in the numerator and the denominator are identical, they cancel each other out completely.

3. Show the solution

• Step 1: Identify the units of the numerator: $\text{kg/m}^3$.
• Step 2: Identify the units of the denominator: $\text{kg/m}^3$.
• Step 3: Perform the division: $\frac{\text{kg/m}^3}{\text{kg/m}^3} = 1$.
• Step 4: Since the units cancel out, the resulting value is a dimensionless quantity. A dimensionless quantity has no unit.

4. Identify the answer

Because relative density is a ratio of two similar physical quantities, it does not have an S.I. unit. Looking at the options provided, option D correctly states this.

5. Exam Tip

Whenever you encounter a physics term that is defined as a "ratio" (like Relative Density, Refractive Index, or Strain), remember that these quantities are dimensionless. They will never have an S.I. unit. This is a common "trick" question in JAMB to test if you understand the definition of physical quantities rather than just memorizing formulas.