Question

Dimension of relative density is-
A. $kg{{m}^{-3}}$
B. $M{{L}^{-3}}$
C. Dimensionless
D. ${{M}^{2}}{{L}^{-6}}$

Answer 1

Hint: First we will discuss what density is and what relative density is. Then we will find the dimensions of density using the formula and then for relative density using the definition of relative density.

Formula used:
Density, $\rho =\dfrac{M}{V}$

Complete step-by-step answer:
Density is defined as the ratio of mass of a body and the volume the body occupies. It defines the mass of a unit volume of material. It can change with change in temperature and pressure. Generally, it increases when pressure is increased as molecules are forced to come closer due to higher pressure and it decreases on increasing the temperature as molecules gain more energy and the bonds holding the material become weaker. This effect is not much for solids and liquids but for gases these effects are easily observable. Different materials will have different densities. The dimensional formula for density will be
$\rho =\dfrac{M}{V}=\dfrac{\left[ M \right]}{\left[ {{L}^{3}} \right]}=\left[ M{{L}^{-3}} \right]$
Relative density is defined as the ratio of density of the material and the density of a reference material. When the reference material is water, relative density is known as specific gravity of the material.
As relative density is the ratio of two densities, it will be a dimensionless quantity.

So, the correct answer is “Option C”.

Note: Difference in density is why two materials of the same shape and size can have different masses. The density of a compound can change throughout its volume if the compound is heterogenous and will be the same throughout the volume if the compound is homogeneous. In the thermodynamics inverse of density known as specific volume is used, it is the ratio of volume and mass of the material and denotes the volume of a unit mass of the material.