Measurement

Measurement is defined as the comparison of unknown quantities with known qualities with the known or standard quantity. Have you ever bought daily used materials like rice, sugar, salt, clothes, etc. from the market? Can they sell these things without measurement? Absolutely No. They sell it by measuring in units (for example rice in kilograms i.e. kg). They sell just after measuring all items and give you as required, this is how measurement is deeply applicable in human life every single day. 

In almost every school, the bell rings after a fixed period of time (45 minutes) according to the daily class routine. Likewise, the earthquake is measured on the Richter scale. The different physical quantities like mass, volume, length, time, the magnitude of an earthquake, etc. are measured by comparing with some standard known quantities called units. Kilogram (kg), liter (l) meter (m), second (s), Richter scale, etc. are some of the units of physical quantities. 

The standard known quantity that is used to measure a physical quantity is called a unit.  

Types of units

The units of the physical quantities have been categorized into two groups. They are:

1. Fundamental Units
2. Derived Units

1. Fundamental Units

The unit of mass is the kilogram, the unit of time is second and the unit of length is meter. The above mentioned physical quantities like time, mass, length, etc. have their own existence. Similarly, their units also do not depend upon other units as well as other units of the measurement do not affect them. Such types of units are called fundamental units. 

 In brief, the fundamental units are defined as: 

Those units of measurement which have their own independent existence and do not depend upon other units are called fundamental units.

 The fundamental units are shown from the given table:

S.N.	Physical quantities	Units	Symbols
1	Length	meter	m
2	Mass	kilogram	kg
3	Time	second	s
4	Temperature	kelvin	K
5	Luminous intensity	candela	cd
6	Electric current	ampere	A
7	Amount of substance	mole	mol

 

2. Derived Units

The unit of density is kg/m³. It includes two fundamental units i.e. kilogram (kg) and meter (m). In the same way, the unit of force is the newton (N) or kgm/s². In this unit, there are three fundamental units i.e. kilogram (kg), meter (m), and second (s). The above units of density and force are derived by the combination of two or more fundamental units. These units fully depend on the fundamental units. Such types of dependent units are called derived units. 

We can define derived units in the following way. 

Those dependent units which are formed by the combination of two or more fundamental units are called derived units.

Some physical quantities, their derived units, and symbols:

Quantities	Formulae	Derived Units	Fundamental Units Involved
Area	length × breadth	meter × meter	m²
Volume	length × breadth × height	meter × meter × meter	m³
Density	mass/volume	kilogram/meter³	kg/m²=kgm¯³
Velocity	displacement/time	meter/second	m/s=ms¯¹
Acceleration	Change in velocity with time	meter/second*second	m/s²
Force	mass*acceleration	kilogram*meter*second¯²or newton	N or kgm/s²
Pressure	force/area	Newton/meter²or Pascal	Kg/ms2 or Pa
Work	force*distance	newton*meter or Joule	kgm²/s²or J
Power	work/time	newton*meter/second or Watt	kgm²/s³or W
Moment	force*distance	newton*meter	kgm²/s²
Frequency	1/second	1/second or Hertz	s¯¹or hertz

In this way, the units which depend upon the fundamental units as well as can be expressed in terms of fundamental units are called derived units.

A standard system of units

In Nepal, some people still use local units like haat and mana for measurement of lengths and mass. These units may vary from place to place. So, in order to maintain uniformity in the measurement of physical quantities, the following standard units are used:

• MKS system: In this system, mass, time, and length are measured in a kilogram, second, and meter respectively. It is also known as the metric system.

• CGS system: In this system, the length is measured in centimeter, mass in gram, and time in second. 

• FPS system: In this system, the length is measured in the foot, mass in the pound, and time in second. 
• SI system: It is described below in brief.

 SI System 

To bring uniformity in the measurement all over the world, a conference of scientists was held in 1960 AD in Paris, the capital of France. The conference introduced the different standard units in the measurement. Now, these standard units are being used all over the world. The system of measurement introduced by the Paris Conference to bring uniformity in measurement all over the world is called the SI system.  Similarly, those standard units of measurement which are introduced by the Paris conference of the scientists held in 1960 AD are called SI units. Its full form is System International de’units.

Why is the SI unit needed? (Importance)

• The international system is a rational system of units. That’s why the system makes use of only one unit for physical quantity.
• It is a coherent system of units. That is, in this system, all the derived units can be easily obtained from fundamental units.
• It is a metric system that multiplies and sub-multiplies can be expressed as powers of 10.