Physics Topics can be challenging to grasp, but the rewards for understanding them are immense.

## Density Overview, Formula & Examples

We will now discuss density and relative density.

Some substances appear to be heavy whereas others are light. For example, iron is heavier than aluminium and water is heavier than alcohol. In physics we describe the lightness or heaviness of different substances by using the word density. The density of a substance is defined as mass of the substance per unit volume. That is :

Density \(=\frac{\text { Mass of the substance }}{\text { Volume of the substance }}\)

Mass of the substance Volume of the substance

The formula for density of a substance can also be written as :

Density \(=\frac{\text { Mass }}{\text { Volume }}\)

The SI unit of mass is kilogram (kg) and the SI unit of volume is cubic metre (m^{3}), so the SI unit of density is ‘kilograms per cubic metre’ (which is written in short form as kg/m^{3} or kg m^{-3}). The values of densities of some of the common substances in SI units are given below :

Densities of Some Common Substances in SI Units

From the above table we can see that the density of water is 1000 kg/m^{3}. By saying that the density of water is 1000 kilograms per cubic metre we mean that the mass of 1 cubic metre volume of water is 1000 kilograms. Please note that the density of water of 1000 kg/m^{3} can also be expressed as 1.0 × 10^{3} kg/m^{3} (by using the powers of 10).

The SI unit of density (kilograms per cubic metre) is a very big unit of density because it involves the mass of 1 cubic metre volume of the substance. So, many times a smaller unit of density called ‘grams per cubic centimetre’ is also used. It is written as g/cm^{3} or g cm^{-3}. When the mass of a substance is taken in ‘grams’ (g) and its volume is taken in ‘cubic centimetres’ (cm^{3}), then its density will come in the unit of ‘grams per cubic centimetre’ (g/cm^{3} or g cm^{-3}). Grams per cubic centimetre is the common unit of density. The densities of some of the substances in common units are given below :

The density of a substance, under specified conditions, is always the same. So, the density of a substance is one of its characteristic properties. The density of a given substance can help us to determine its purity. We will study this in higher classes. Please note that if the density of a substance is more than the density of water, then the substance will be heavier than water and hence sink in water. On the other hand, if the density of a substance is less than the density of water, then the substance will be lighter than water and hence float in water. We will now solve some numerical problems based on density.

**Example Problem 1.**

The mass of 2 m^{3} of steel is 15600 kg. Calculate the density of steel in SI units.

**Solution.**

We know that:

Density \(=\frac{\text { Mass }}{\text { Volume }}\)

\(=\frac{15600 \mathrm{~kg}}{2 \mathrm{~m}^3}\)

= 7800 kg/m^{3}

Thus, the density of steel in SI units is 7800 kg/m^{3}.

**Example Problem 2.**

An object of mass 50 g has a volume of 20 cm^{3}. Calculate the density of the object. If the density of water be 1 g/cm^{3}, state whether the object will float or sink in water.

**Solution.**

We know that :

Density \(=\frac{\text { Mass of the object }}{\text { Volume of the object }}\)

Here, Mass of the object = 50 g

And, Volume of the object = 20 cm^{3}

Now, putting these values of mass and volume of the object in the above formula, we get :

Density of object = \(\frac{50 \mathrm{~g}}{20 \mathrm{~cm}^3}\)

= 2.5 g/cm^{3}

Thus, the density of object is 2.5 g/cm^{3}.

Since the density of object (2.5 g/cm^{3}) is greater than the density of water (1 g/cm^{3}), therefore, the object will sink in water.