What is Density and How is it Calculated?

The term ‘Density’ refers to the measure of the mass of an object or body having unit volume. It is denoted by the symbol ρ or can be simply represented by the letter D.

Quantitatively, density is mass divided by volume.

The density of a given material shows its denseness in a specific area. It is usually a measure of how tightly the particles of matter are packed together.

Greek scientist Archimedes discovered the principle of density. The density of an object shows how heavy it is at a constant volume.

Mathematically, the density of an object can be calculated with the help of the formula specified below:

Density = Mass/Volume or ρ = m/v, where ρ = Density, m = mass, and v = volume.

Solids are typically denser than liquids and gases as the particles are tightly packed with very little space among them. In liquids, particles are not very tightly packed, due to which, they are less dense than solids but denser than gases, which have free-flowing particles.

Types of Density

Usually, the density is of 2 types, one is absolute density, and the other is relative density. Relative density is also known as specific gravity, which is the ratio of the density of a material to the density of reference material. Usually, the reference material is water. Specific gravity is a relative quantity with no units.

Absolute density refers to the mass of any substance per unit volume of a material. It is usually expressed in g/cm3.

To find the density of an object, measure the mass of the material and divide it by the volume it covers, since the density of water is 1 gm/cm³ - the ratio of the density of the material to that of water is 1:£ (Density of water is 1 gm/cm³ at 4°C.)

For example, the density of gold is 19.32 g/cm³, and so the specific gravity is 19.32.

Units of Density

Units of density are g/cm³

The SI units of density are kg/m³.

Other density units - Gram /litre (g/l),

Gram /millilitres

Applications of Density in Real Life

Let's get an idea with an example from real life.

Suppose you have two balloons. One is filled with air, and the other one is filled with coke. Coke is much denser because the atoms take up less space as they move around less. The air balloon contains atoms that are colliding around very quickly, and this makes the atoms take up more space or less density. Thus, the balloon with air is light and the balloon with water is heavy.

Usually, density plays a crucial role in many applications, life tubes we find on beaches or in swimming pools are designed to float on water so that people can swim without sinking, just by holding those air-filled tubes. Life tubes are filled with air which is less dense than water so it always floats. Another application is, ships can float because they have ballast tanks that hold air, and these tanks provide large volumes with little mass, hence decreasing the density of the ship. Combined with the buoyant force, this reduced density helps the ship to float over water. Submarines dive below the surface of the water by emptying their ballast tanks.

Solved Examples

Question 1:

Calculate the density of water if it has a volume of 1m3 and mass of 1160 Kg.

Answer 1

Given:

Mass = m = 1160 Kg

Volume = v = 1m3

To find:

Density

Solution:

Density = Mass/Volume = ρ = m/v

Density = 1160/1

Density = ρ = 1160 kg/m3

Question 2

You have a rock with mass 60g and density 2 g/cm3. Calculate its volume.

Answer 2

We know that Density = ρ = Mass/Volume

Volume = v = Mass/Density

Let’s substitute the values given.

Volume = 60/2 = 30cm3

Question 3

If the density of diamond is 3.5 g/cm3, what will be the mass of diamond having a volume of 0.5 cm3?

Answer 3

Given:

Density = ρ = 3.5 g/cm3

Volume = v = 0.5 cm3

To find:

Mass or m

Solution:

We know that Density = mass/volume

Mass = Density * volume

Let’s substitute the values and find the value of Mass

Mass = 3.5 * 0.5

Mass = 1.8g