Question

Explain density and relative density and write formulae.

Answer 1

Hint: The density of the substance relates it mass and volume.
The relative density relates the density of the substance with density of water.

Complete step by step answer:
We know that the density of a substance is the ratio of the mass of the substance and its volume. It is often denoted by the lowercase Greek letter \[\rho \]. We can express the density of substance of mass m and volume V as,
\[\rho = \dfrac{m}{V}\]
From the above formula, we can observe that the density of the substance will be high if its mass is concentrated in less volume.
An S.I. unit of density is \[kg/{m^3}\]. The dimensional formula for density is \[\left[ {{{\text{L}}^{ - 3}}\,{{\text{M}}^1}\,{{\text{T}}^0}} \right]\].
We can express the density of the sphere of mass m and radius R as follows,
\[\rho = \dfrac{m}{{\dfrac{4}{3}\pi {R^3}}}\]
We know that the density of water is \[1000\,kg/{m^3}\] or \[1\,g/c{m^3}\]. This means that 1 gram of water can be fit into a vessel of volume \[1\,c{m^3}\].
The relative density of a substance is defined as the ratio of density of that substance to the density of water. We can write the formula for relative density as below,
\[{\text{R}}{\text{.D}}{\text{.}} = \dfrac{{{\text{Density of substance}}}}{{{\text{Density of water}}}}\]

Relative density of any liquid is less than one because the density of water is greater than any liquid. The relative density is unit less quantity.
The relative density of solids can be greater than one. Osmium and Iridium are the elements with highest relative density.

Note:
Students should remember that the density has units but the relative density is unit less. Relative density can be determined if and only if the density of the substance is known to us. Density of almost every object can be calculated including the planets in our solar system if their mass and radius is known to us.