Unit of Density - Meaning, Definition, Example, Unit, Formula FAQs

What is Density?

Density is the measure of how much mass is contained in a given volume of a substance. It tells us how tightly the matter is packed in an object.

Density = how heavy something is for its size.

Formula:

$
\text { Density }=\frac{\text { Mass }}{\text { Volume }}
$

SI Unit:
The SI unit of density is kilogram per cubic metre ( $\mathbf{k g} / \mathbf{m}^{\mathbf{3}}$ ).
Example:
If two cubes of the same size are made of iron and wood, the iron cube feels heavier because iron has a higher density than wood - it has more mass in the same volume.

Common Densities:
Water: $1000 \mathrm{~kg} / \mathrm{m}^3$
Air: $1.29 \mathrm{~kg} / \mathrm{m}^3$
Iron: $7870 \mathrm{~kg} / \mathrm{m}^3$

Density example:

Dense materials include iron, platinum, and lead. Dense stuff includes a variety of rocks and minerals. Dense materials are more likely to ‘feel' weighty or rigid. Sparse is the polar opposite of dense, and examples of sparse materials include glass, bamboo, aluminium, and styrofoam. Liquids have a lower density than solids, while gases have a lower density than liquids. This is because solids have closely packed particles, liquids have materials that allow particles to slide around one another, and gases have particles that are free to move around.

Units of Density

The SI unit of density is:$
\text { kilogram per cubic metre }\left(\mathrm{kg} / \mathrm{m}^3\right)
$

This means the mass is measured in kilograms ( $\mathbf{k g}$ ) and the volume in cubic metres ( $\mathrm{m}^3$ ).

Other Common Units:

How Is Density Calculated?

Density is calculated by dividing the mass of a substance by its volume.

$
\text { Density }(\rho)=\frac{\text { Mass }(\mathrm{m})}{\text { Volume }(\mathrm{V})}
$
Where:

• $\boldsymbol{\rho}$ (rho) $=$ density
• $\mathbf{m}=$ mass of the object
• $\mathbf{V}=$ volume of the object

Steps to Calculate Density:
1. Measure the mass of the object using a balance (in kilograms or grams).
2. Find the volume of the object.

• For regular shapes: use mathematical formulas (e.g., cube: $V=l^3$, cylinder: $V=\pi r^2 h$ )
• For irregular objects: use the water displacement method.

3. Divide mass by volume to get density.

Application of density in real life:

• Floating and sinking: Objects float if their density is less than water.
• Ship design: Ships float because their overall density is low.
• Hot air balloons: Hot air is less dense, so balloons rise.
• Oil and water: Oil floats on water as it is less dense.
• Identifying materials: Density helps find what a substance is made of.

Solved Examples on Density

Example 1:
Question: A metal block has a mass of 600 g and a volume of $200 \mathrm{~cm}^3$. Find its density.
Solution:

$
\text { Density }=\frac{\text { Mass }}{\text { Volume }}=\frac{600 \mathrm{~g}}{200 \mathrm{~cm}^3}=3 \mathrm{~g} / \mathrm{cm}^3
$

Answer: $\mathbf{3 ~ g / c m}{ }^{\mathbf{3}}$

Example 2:
Question: A wooden cube has a side of 0.2 m and mass 8 kg . Calculate its density.
Solution:

$
\begin{aligned}
& \text { Volume of cube }=\operatorname{side}^3=0.2^3=0.008 \mathrm{~m}^3 \\
& \text { Density }=\frac{\text { Mass }}{\text { Volume }}=\frac{8}{0.008}=1000 \mathrm{~kg} / \mathrm{m}^3
\end{aligned}
$

Answer: $\mathbf{1 0 0 0 ~ k g / m ³}$

Example 3:
Question: An object of mass 50 g sinks in water. If its volume is $40 \mathrm{~cm}^3$, find its density.
Solution:

$
\text { Density }=\frac{50}{40}=1.25 \mathrm{~g} / \mathrm{cm}^3
$

Answer: $\mathbf{1 . 2 5 ~ g} / \mathbf{c m}^{\mathbf{3}}$

Also check-

• NCERT Exemplar Class 11th Physics Solutions
• NCERT Exemplar Class 12th Physics Solutions
• NCERT Exemplar Solutions for All Subjects

NCERT Physics Notes:

• NCERT Notes Class 11th Physics
• NCERT Notes Class 12th Physics
• NCERT Notes For All Subjects

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