Every measurement in Physics begins with identifying what we want to measure and choosing an appropriate standard for comparison. Whether we measure the length of a pen, the mass of an object, or the time taken by a moving body, we use physical quantities and units to express the result accurately. In this Class 11 Physics lesson on Units and Measurement, you will learn what physical quantities are, how fundamental and derived quantities differ, why standard units are necessary, and how systems of units such as CGS, FPS, MKS, and SI are used in Physics.
Learning Objectives
After studying this lesson, you will be able to:
- Define physical quantities and units.
- Distinguish between fundamental (base) quantities and derived quantities.
- Explain the importance of standard units in measurement.
- Identify the essential characteristics of a good unit.
- Differentiate between base units and derived units.
- Describe the CGS, FPS, MKS, and SI systems of units.
- Identify the seven base quantities and their SI units.
Video Lesson
Watch the video for a detailed explanation and examples.
Quick Revision
| Concept | Meaning | Example |
|---|---|---|
| Physical Quantity | A property that can be measured and expressed numerically with a unit | Length, mass, time |
| Fundamental Quantity | A base quantity independent of the other base quantities | Length, mass, time |
| Derived Quantity | A quantity expressed in terms of base quantities | Speed, force, density |
| Unit | An agreed standard used to measure a physical quantity | Metre, kilogram, second |
| Base Unit | SI unit assigned to a base quantity | Metre (m) for length |
| Derived Unit | Unit expressed in terms of base units | Metre per second (m/s) for speed |
| System of Units | A consistent collection of units used for measurement | CGS, MKS, SI |
What are Physical Quantities?
A physical quantity is a measurable property of a body, substance, or physical phenomenon that can be expressed by a numerical value and a unit.
For example, the length of a pen, the mass of a book, the temperature of water, and the time taken to complete a journey are physical quantities.
A measurement generally consists of two parts:
Physical quantity = Numerical value × Unit
For example:
Length = 20 cm
Here:
- Physical quantity: Length
- Numerical value: 20
- Unit: centimetre (cm)
The numerical value alone is not sufficient to describe a measurement. The unit is also necessary to communicate the result clearly.
Physical quantities are classified into two main categories:
- Fundamental or base quantities
- Derived quantities
Fundamental or Base Quantities
Fundamental quantities, also called base quantities, are a selected set of quantities that form the foundation for expressing other physical quantities.
In the International System of Units (SI), there are seven base quantities.
| Base Quantity | SI Base Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
These quantities are treated as independent of one another in the SI system. Other physical quantities can be expressed using combinations of these base quantities.
For example, length, mass, and time are used to express many quantities in mechanics.
Derived Quantities
Derived quantities are physical quantities expressed in terms of base quantities through mathematical relationships.
They are obtained by multiplying, dividing, or otherwise combining base quantities.
Examples of Derived Quantities
1. Area
Area is the product of length and breadth.
Area = Length × Breadth
SI unit: square metre ($m^2$)
2. Volume
Volume is the product of length, breadth, and height.
Volume = l × b × h
SI unit: cubic metre ($m^3$)
3. Speed
Speed is the distance travelled per unit time.
$$Speed = \frac{{Distance}}{{Time}}$$
SI unit: metre per second (m/s)
4. Density
Density is mass per unit volume.
$$Density = \frac{{Mass}}{{Volume}}$$
SI unit: kilogram per cubic metre ($kg/m^3$)
5. Force
According to Newton’s second law, force is the product of mass and acceleration.
F = ma
SI unit: newton (N), where $1N = 1 kg m/s^2$
These examples show how derived quantities and their units can be expressed using base quantities and base units.
Difference Between Fundamental and Derived Quantities
| Fundamental Quantities | Derived Quantities |
|---|---|
| Form the selected basis of a system of quantities | Expressed in terms of base quantities |
| Treated as independent base quantities | Depend on relationships involving base quantities |
| Have corresponding base units in SI | Have corresponding derived units |
| Examples: length, mass, time | Examples: area, speed, force |
Remember: The distinction between base and derived quantities depends on the system of quantities being used. In the SI system, seven quantities are designated as base quantities.
What are Units?
A unit is an agreed standard used to measure a physical quantity.
For example, when we say that the length of a table is 2 metres, the metre is the unit used to express the measurement.
Without standard units, measurements made by different people or in different places would be difficult to compare.
Imagine two people measuring the same table using their hand spans. They may obtain different numerical results because their hand spans are different. Using a standard unit such as the metre makes the measurement consistent and understandable.
A physical measurement is expressed as:
Q = n × u
where:
- Q = physical quantity
- n = numerical value
- u = unit
For example, for a length of 5 metres:
Q = 5 × 1 m = 5 m
Characteristics of a Good Standard Unit
A standard unit should have the following characteristics:
- Well-defined: Its meaning and method of realization should be clearly specified.
- Invariable and reproducible: It should provide consistent results across different times and places.
- Convenient: It should be practical to use in measurements.
- Universally accessible or realizable: It should be possible to reproduce or realize the standard wherever accurate measurement is required.
Modern SI units are defined using fixed physical constants and specified realization procedures. This makes them more reliable and reproducible than standards based on physical objects that may change over time.
Fundamental Units and Derived Units
Units are classified according to the quantities they measure.
1. Fundamental or Base Units
Base units are the units assigned to the seven base quantities in the SI system.
Examples:
- Length — metre (m)
- Mass — kilogram (kg)
- Time — second (s)
- Electric current — ampere (A)
2. Derived Units
Derived units are formed by combining base units according to the defining equations of derived quantities.
Examples:
- Area — $m^2$
- Volume — $m^3$
- Speed — m/s
- Acceleration — $m/s^2$
- Force — newton (N)
- Work — joule (J)
- Pressure — pascal (Pa)
For example, since force equals mass multiplied by acceleration,
F = ma
the SI unit of force is:
$$kg \frac{{m}}{{s}^2 = kg m/s^2$$
This unit is given the special name newton (N).
What is a System of Units?
A system of units is a consistent collection of units used to measure physical quantities.
Different systems were developed historically to standardize measurements. The major systems commonly discussed in introductory Physics are CGS, FPS, MKS, and SI.
1. CGS System
CGS stands for centimetre–gram–second.
The basic units of length, mass, and time are:
- Length — centimetre (cm)
- Mass — gram (g)
- Time — second (s)
2. FPS System
FPS stands for foot–pound–second.
In the traditional FPS system, the basic units are:
- Length — foot (ft)
- Mass — pound (lb), in the mass-based version
- Time — second (s)
Note: Some FPS engineering systems use pound-force and require careful distinction between mass and force.
3. MKS System
MKS stands for metre–kilogram–second.
Its basic units are:
- Length — metre (m)
- Mass — kilogram (kg)
- Time — second (s)
The MKS system provided an important foundation for the development of the International System of Units.
4. SI System
SI stands for the International System of Units. It is the internationally accepted system used in science, technology, and most areas of everyday measurement.
The SI system has seven base units corresponding to its seven base quantities. Derived units are formed from these base units.
Examples include:
- Metre (m) — length
- Kilogram (kg) — mass
- Second (s) — time
- Ampere (A) — electric current
- Kelvin (K) — thermodynamic temperature
- Mole (mol) — amount of substance
- Candela (cd) — luminous intensity
The SI system provides a common standard that enables scientists, engineers, students, and researchers around the world to communicate measurements consistently.
Comparison of Different Systems of Units
| System | Full Form | Unit of Length | Unit of Mass | Unit of Time |
|---|---|---|---|---|
| CGS | Centimetre–Gram–Second | Centimetre (cm) | Gram (g) | Second (s) |
| FPS | Foot–Pound–Second | Foot (ft) | Pound (lb) | Second (s) |
| MKS | Metre–Kilogram–Second | Metre (m) | Kilogram (kg) | Second (s) |
| SI | International System of Units | Metre (m) | Kilogram (kg) | Second (s) |
Important: SI is a comprehensive international system containing seven base units, not merely a system based on length, mass, and time.
Practice Questions
Short Answer Questions
- What is a physical quantity? Give two examples.
- What is a unit? Why are standard units necessary?
- Define fundamental or base quantities.
- What are derived quantities? Give three examples.
- List the seven SI base quantities and their units.
- What are the characteristics of a good standard unit?
- What is meant by a system of units?
- Expand CGS, FPS, MKS, and SI.
Conceptual Questions
- Distinguish between fundamental quantities and derived quantities with examples.
- Explain the difference between a base unit and a derived unit.
- Why is the SI system preferred for scientific measurements?
- Why is the metre a base unit while the metre per second is a derived unit?
- Explain why a numerical value without a unit may be insufficient to communicate a measurement.
Application Questions
- Express the unit of speed in terms of SI base units.
- Express the unit of force in terms of SI base units.
- Identify the physical quantity and its unit in the measurement 25 kg.
- State the system of units in which length is measured in centimetres and mass in grams.
Frequently Asked Questions (FAQs)
Key Points to Remember
- A physical quantity is a measurable property expressed using a numerical value and a unit.
- A unit is a standard used to measure a physical quantity.
- SI has seven base quantities and seven corresponding base units.
- Derived quantities are expressed in terms of base quantities.
- Derived units are formed by combining base units.
- A good standard unit should be well-defined, reproducible, convenient, and capable of consistent realization.
- CGS stands for centimetre–gram–second.
- FPS stands for foot–pound–second.
- MKS stands for metre–kilogram–second.
- SI stands for International System of Units.
- SI provides a common international standard for scientific measurements.
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