**Matter exists in three states solid, liquid and gas. Any state of matter that can flow is a fluid. Liquids and gases are therefore, referred to as fluids.**

__Density :__

__Density :__**Density of a substance is the mass per unit volume. Homogenous bodies have uniform density:**

**The unit of density is kg/m3 in S.I. system. Dimension of density is given by [ρ] = = [M] [L ^{-3}].**

__Relative Density or Specific Gravity :__

__Relative Density or Specific Gravity :__**Relative density of a substance is the ratio of the density of the substance to the density of pure water (ρ _{w} = 1000 kg/m3) at 4°C.**

**“Relative density is dimensionless “**

**Illustration : A hollow metallic sphere has inner and outer radii respectively as 5 cm and 10 cm. If the mass of the sphere is 2.5 kg, find (a) density of the material (b) relative density of the material of the sphere.**

**Solution: The volume of the material of the sphere is**

**= 0.00367 m ^{3}**

**(a) Therefore, density of the material of the sphere is**

**= 681.2 kg/m ^{3}**

**(b) **

**= 0.6812**

__Density of a mixture__

__Density of a mixture__**Let a number of substances of masses M1, M2, M3 etc., and densities ρ _{1}, ρ_{2}, ρ_{3}, etc. respectively be mixed together.**

**The total mass of the mixture is = M _{1} + M_{2} + M_{3} + ….**

**The total volume ;**

**provided that the substances retain their individual states within the mixture.**

**Therefore, the density of the mixture is**

**The same expression may written in terms of the volumes:**

**The density of the mixture is**

**where V _{1}, V_{2}, V_{3} … represent the volumes of substances of densities ρ_{1}, ρ_{2}, ρ_{3} . . . in the mixture**

**Illustration : Two liquids of densities 2.5 gm/cm ^{3} and 0.8 gm/cm^{3} are taken in the ratio of their masses as 2:3 respectively. Find the average density of the liquid combination.**

**Solution: Let the masses be ‘ 2 m ‘ gm and ‘ 3 m ‘ gm respectively.**

**Therefore, the volume of the first liquid of density 2.5 gm/cm ^{3} is V_{1} = 2m/2.5 cm^{3}**

**That of the second liquid is V _{2} = 3m/0.8 cm^{3}**

**Total volume **

**Total mass = 2m + 3m = 5 m gm**

**Therefore, the average density**

**= 1.09 gm/cm ^{3}**

**Exercise : Two miscible liquids of densities 1.2 gm/cc and 1.4 gm/cc are mixed with a proportion ratio of their volumes equal to 3:5. What is the density of resulting liquid?**