Question

Which among the following physical quantities does not possess a unit?

• A. Area
• B. Volume
• C. Density
• D. Specific gravity

Answer 1

The correct option is D

Specific gravity

Explanation for incorrect option:

1. Area = Length(m) x width(m) {On calculating the unit of the area would be m². }
2. Volume = Length(m) x width(m) x height(m) {On calculating the unit of the volume would be m³.}
3. $Density=\frac{Mass\left(kg\right)}{Volume\left(m^3\right)}${On calculating the unit of density would be kg/m^3.}

Explanation for correct option:

1. Specific Gravity${\mathrm{\rho }}_{\mathrm{specific}\mathrm{gravity}}=\frac{{\mathrm{\rho }}_{\mathrm{unknown}}(\mathrm{kg}/{\mathrm{m}}^3)}{{\mathrm{\rho }}_{\mathrm{standard}}(\mathrm{kg}/{\mathrm{m}}^3)}$

$\because$Specific gravity is the ratio of the density of the given substance to the density of the standard substance. Since, the specific gravity is the ratio of the like quantities, it has no unit.

Hence, the specific gravity has no unit. Thus option (d) is correct.