Question

The density of a metal is $10.8\; \times {10^{3\;}}\,kg.{m^{ - 3}}$. Find the relative density of the metal.

Answer 1

Density of a substance is given by the ratio of the mass of the substance to the volume of the substance. Relative density of a substance is given by the ratio of the density of the substance to the density of water.

Formula used:
Mathematically density of an object is given by,
$d = \dfrac{m}{V}$
where, $m$ is the mass of the object and $V$ is the volume of the object.
Relative density of a substance is given by,
${d_{rel}} = \dfrac{d}{{{d_{water}}}}$
where, $d$ is the density of the substance, ${d_{water}}$ is the density of the water and ${d_{rel}}$ is the relative density of the substance.

Complete step by step answer:
We know that, density of a substance is given by the ratio of the mass of the substance to the volume of the substance and relative density of a substance is given by the ratio of the density of the substance to the density of water. Here given that, the density of the metal is $10.8\; \times {10^{3\;}}\,kg.{m^{ - 3}}$. Now, the density of water is given by, ${10^{3\;}}\,kg.{m^{ - 3}}$.

Hence, the relative density of the material is the ratio of the density of the substance to the density of water. So, putting the value of the density of the metal and the density of water we get the relative density of the substance as,
${d_{rel}} = \dfrac{{10.8\; \times {{10}^{3\;}}\,}}{{{{10}^{3\;}}}}$
$\therefore {d_{rel}} = 10.8$

Hence, the relative density of the metal is $10.8$.

Note: The relative density of any substance is a dimensionless quantity since it is a ratio of two densities. To find the density of water use the fact that the weight of water at ${4^ \circ }C$ is $1gm\,per\,cc$. Since, the relative density is just a number it is useful in comparative study of density of different substances.