Question

The SI unit of relative density is kg/$m^3$. True or false.
(A.) True
(B). False

Answer 1

- Hint: Recall of density and relative density. Then compare the difference between them. After that recall, the mathematical expression used to calculate density and relative density. Then using the mathematical expression find their units.

Complete step-by-step solution -

The density of a substance is the ratio of mass contained in the substance to the volume of the substance. The symbol of density is ρ(rho). In mathematical terms, we can write density as:
$\rho=\dfrac{m}{V}$
where,
m is the mass of the body and V is the volume of the body. SI unit of mass is the kilogram(kg) and volume is cubic meter($m^3$). Thus, its SI unit of density is kg/$m^3$.

Relative density is the ratio of the density of unknown material to the density of the known material. In general, the known material if not specified is taken to be water. In mathematical terms, relative density is given as:
$R . D .=\dfrac{\rho_{u n k n o w n}}{\rho_{k n o w n}}$

Thus, we can conclude that relative density is unit-less. That is, it does not have any units. So, the given statement is false.

Additional Information:
There are few factors other than mass and volume that affect density like:
1. Temperature
2. Pressure

Densities of few common substances are given as:
-Pure water has a density of 1 g/$cm^3$.
- Water (20 degrees Celsius) has a density of 0.998 g/$cm^3$.
-Ethanol has a density of 0.810 g/$cm^3$.
-Benzene has a density of 0.900 g/$cm^3$.
- Iron has a density of 7.8 g/$cm^3$.
-Gold has a density of 19.3 g/$cm^3$.

Relative density is used for the following purposes:
-It is used by geologists.
-It is used to measure buoyancy.
-It is used by mineralogists.

Note: Do not get confused between the terms density and relative density. SI unit of density is kg/$m^3$ but relative density is unitless. Thus, True in incorrect option.
Specific gravity is also known as relative density. So, specific gravity also does not have any units.