Meaning, Definition, SI Unit, Solved Examples

Density Formula: Density Formula is the measurement of the amount of mass per unit of volume. Density refers to the measurement of relative compactness. The definition of this physical quantity can be expressed as mass (m) in a particular volume (v). Most significant, the symbol ρ is used to express this measurement. Moreover, this symbol happens to be the lowercase Greek letter rho. Density is symbolized by D. and the formula of Density is Density= Mass/ Volume.

Density= Mass/ Volume

ρ = m/V

Where,

ρ = Density of material

m = Mass of material

V = Volume of material

What is Density?

The density of material shows the amount of denseness of the material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly a matter can be packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the its related units The symbol ρ represents density or it can also be represented by the letter D.

Density Formula

The density formula for solids, liquids, and gas molecules is the measurement of mass per unit volume at a given temperature and pressure. In chemistry or physics, density is expressed by the symbol ρ or D. Mathematically density is expressed by the formula, ρ = m/V.

where m = mass of the substance and V = volume.

ρ = m/V

ρ = density, ( it can be in kg/m³, or g/(cm³)

m = mass, ( it can be in kg or g)

V = volume, ( it can be in m³ or cm³)

Here, ρ = density, m = mass, and v = volume.

Dimensional Formula of Density

The dimensional formula of density is: [M1 L-3 T0]

Where

M= Mass

L= Length

T= Time

SI Unit of Density Formula

Each substance has some amount of specific density. Generally, the density of water (which is approximately about 1 gram/cubic centimeter) is taken as the standard value for calculating the density of substances. However, the SI unit of Density formula is measured using kilograms per cubic meter (kg/m³).

Density Examples in Daily Life

There are many examples in our daily life where application of density are used, some of the example are pipe design, shipbuilding, helium balloons, weight distribution in an airplane, and the fact that ice floats on water.

• The knowledge of the densities of two substances helps you in separation techniques. For example, the separation of oil from water. If there is a leakage of an oil tank in the ocean then oil drops start to float on the water due to less density than the water.
• Another well-known application of density is determining whether an object will float on water or not. The floating of ships and diving of submarines are due to their density difference.

Solved Examples of Density Formula

Q1. Calculate the density of water if it has a mass of 1000 Kg and a volume of 1 m³.

Solution: Given, Mass = 1000 Kg, Volume = 1m³

Density is given by the formula:

Density = Mass/Volume

ρ = 1000/1 = 1000 kg/m³

Q2. If you find a shiny rock, a carbon allotrope with a volume of 0.042cm³ and a mass of 0.14 g, is it graphite or diamond? The density of graphite is 2.266 g/cm³ and the density of diamond is 3.51g/cm³.

Solution: Given,

Volume of the shiny rock =0.042 cm³

Mass of the shiny rock = 0.14 g

Density of graphite = 2.266 g/cm³

Density of diamond = 3.51g/cm³

Use the density equation to solve for m, for the mass of graphite and for the mass of a diamond.

ρ = m/V

m = ρV

m = 2.266 g/cm³ x 0.042 cm³ = 0.0951g for graphite

m = 3.51g/cm³ x 0.042 cm³ = 0.1474 g for diamond

The mass of the shiny rock you found is identical to the mass of a diamond.

Q3. You have a different rock with a volume of 30cm³ and a mass of 60g. What is its density?

Solution: Density is mass divided by volume so the density is 60 g divided by 30cm³, which is 2.0 g/cm³.

Q4. You decide you want to carry a boulder home from the beach. It is 30 centimeters on each side, and so has a volume of 27,000 cm³. It is made of granite, which has a typical density of 2.8 g/cm³. How much will this boulder weigh?

Solution:

In this case, you are asked for a mass, not the density. You will need to rearrange the density equation so that you get mass.

Density= Mass/ Volume

By multiplying both sides by volume, the mass will be left alone.

Mass= Volume X Density

Substituting the values from the problem,

Mass= 27000cm³ X 2.8 g/cm³

The result is that the mass is 75,600 grams.

Q5. Rocks are sometimes used along coasts to prevent erosion. If a rock needs to weigh 2,000 kilograms (about 2 tons) in order not to be shifted by waves, how big (what volume) does it need to be? You are using basalt, which has a typical density of 3200 kg/m³

Solution:

In this problem, you need a volume, so you will need to rearrange the density equation to get volume.

Density = Mass/ Volume

By multiplying both sides by volume, we can get volume out of the numerator (the bottom).

Volume x Density = Mass

You can then divide both sides by density to get volume alone:

Volume = Mass/ Density

By substituting in the values listed above,

Volume = 2000 kg/ 3200 kg/m³

So the volume will be 0.625 m³.