[Physics Class Notes] on Unit of Density Pdf for Exam

The measure of the denseness in a specific given area of a material is known as its density. It is basically a measure of how tightly matter is packed together. It is a unique property of an object. Archimedes, a Greek scientist, discovered the principle of density. By knowing the formulas and the units, one can easily calculate the density of an object. It is most commonly denoted by or sometimes D.

Density- Examples

Heavy or hard materials are supposed to be dense such as iron, platinum, rocks, minerals, and so on. Materials like glass, bamboo, styrofoam are not dense materials. In matter, liquids are denser than gases and solids are denser than liquids. In the case of gases, particles can move freely all over the place while in the case of solids particles can collide with each other.

Density- Formula

Density is calculated by mass over volume, which can be written as-

[Density = frac{Mass}{Volume}]

[rho = frac{m}{v}]

where [rho] denotes density

m denotes mass and v volume

Density- SI and Other Units

The density of all different substances is also different which means the density of substances would weigh differently for the same volume of different substances. Therefore, the density of each substance is specific. The standard value for calculating density is taken as 1 g/cm³ which is the approximate density of water. Though, the SI unit of density is taken as kg/m³.

Density can also be expressed in terms of liters, metric tons, as listed below-

• t/m³– metric ton per cubic meter

• g/mL- gram per milliliter

• kg/L- kilogram per liter

• g/cm³– gram per cubic centimeter

• mg/m³– megagram per cubic meter

• kg/dm³– kilogram per cubic decimeter

In the CGS system, the density of objects is measured in g/cm³.

Types of Density

Usually, the density is of two 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

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

Ans: Given-

Mass = m = 1160 Kg

Volume = v = 1m³

Solution:

[Density = frac{Mass}{Volume}][rho = frac{m}{v}]

Density = 1160/1

Density = ρ = 1160 kg/m³

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

Ans: We know that Density = ρ = Mass/Volume 

Volume = v = Mass/Density

Let’s substitute the values given.

Volume  = 60/2 = 30cm³

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?

Ans: Given:

Density = ρ = 3.5 g/cm³

Volume = v = 0.5 cm³

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