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Units and Measurements

Physics is the study of nature and natural phenomena. While studying natural phenomena, we come across several physical quantities such as mass, velocity, force, etc., which are measurable. Quantities such as beauty of a flower, feeling of happiness, etc., are not measurable as they are subjective. In physics, we deal with one measurable quantity called physical quantity. By studying nature, we discover principles and laws that help us to analyse and understand natural phenomena. Measurement helps us in quantifying the physical quantities in nature.

Matter is anything that has mass and occupies space. It is the interaction of matter and energy that creates all the physical phenomena. We shall begin our journey of understanding nature through defining physical quantities and measuring them.

Physical Quantity

A quantity that can be measured is called a physical quantity, namely length, mass, force, pressure, time, temperature, etc.

Are there quantities that cannot be measured? How about the following? Beauty of a flower, innocence of a child, passion for learning, etc. These are not measurable.

How Many Physical Quantities Are There in All?
We can define a number of them. But only seven fundamental quantities that are independent of each other are sufficient to define any other physical quantity.
They are length, mass, time, temperature, amount of substance, electric current and luminous intensity. All other physical quantities can be derived from these seven fundamental quantities.

Speed = Description: 35774.png or Area = Length × Breadth.


Such quantities are called ‘derived quantities’.
How Can Physical Quantities Be Measured?
Observe that you measure the length of a cloth by comparing it with a standard length of a metre or you measure the mass of an object by comparing its mass with that of a standard kilogram.
Measurement is the process of comparison of a given physical quantity with a chosen standard of the same kind.
The chosen standards such as a metre or a kilogram are called units.
If a cloth’s length measures 3.5 times the length of a metre stick, you say its length is 3.5 metres, represented as 3.5 m. If an object is 2.2 times the standard kilogram, we say the mass of the object is 2.2 kilogram or 2.2 kg.
The following table gives the units and their symbols for the seven fundamental quantities.

Fundamental Quantity





metre (m)

centimetre (cm)

foot (ft)


kilogram (kg)

gram (g)

pound (lb)


second (s)

second (s)

second (s)


kelvin (K)

celsius (°C)

Fahrenheit (°F)

Electric current

ampere (A)



Luminous intensity

candela (cd)



Amount of substance





SI: Systeme International D’Units (system international, a universally accepted system of units). For details, refer www.bipm.org
CGS: centimetre, gram, second system
FPS: foot, pound, second system
Note: that the symbols of units are written in small letters (kg, s, m, etc,), except for kelvin (K) and ampere (A) as they are named after scientists Kelvin and Ampere, respectively.

Results of Measurement
Look at the following results of measurement.
The building is 10 m tall.
The room temperature is 25°C.
It takes 15 min to reach school from home.
The result of every measurement has two parts: a number and a unit. Without either of them, the result cannot be comprehended.
Any physical quantity has two parts:
  1. A number expressing its magnitude (how big or small) and
  2. a unit (which indicates the type of the quantity such as length, area, volume, etc.)
The units in calculation have to be treated just like any other algebraic quantities.

Let us calculate the volume of the earth (radius of earth R = 6.37 × 106 m).


Assuming earth to be spherical, the volume of earth is given by


Description: 35824.png


Description: 35831.png


Description: 35839.png


= (1.08 × 1021) m3


If you want to express this as kilometre, it can be done this way!


Description: 35850.png


Description: 35861.png


Description: 35875.png


(the m3 term in the numerator and the denominator gets cancelled)


= 1.08 × 1012 km3

The two most important tasks in any calculations in physics are keeping track of the units in an equation and doing the conversions between different systems of units.

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