## Introduction

**Units and Measurement |** We know *physics* is an experimental science. To understand experimental science like physics, we associate our theoretical description of nature with our experimental observation of nature through quantitative measurement. In physics, we deal with numerous physical quantities, such as mass, length, time, velocity, force, pressure, etc.

These physical quantities can give clear understanding only if we can measure them into these measurements. That’s why, sometimes physics is called the *science* of measurement.

For example, when we drop an object from a certain height, it falls down on the surface of the earth. To understand this natural phenomenon, we must know the following things:

- Why does the object fall on the surface of the earth?
- With what velocity does it fall?
- The object takes how much time to reach the ground? And so on.
- To answer all these questions, we will need the measurement of distance, time, mass, etc.

In this chapter, we will discuss **units and measurement** as well as make notes for class 11 based on the NCERT syllabus.

## Table of Contents

## Physical Quantity

The quantities which we can define or measure are called physical quantities. For example, mass, length, volume of an object, speed of moving car, distance, force, time, current, etc. are the examples of physical quantities. We describe the laws of physics in the terms of these physical quantities.

There are two types of physical quantities in physics. They are:

- Fundamental quantities
- Derived quantities

Fundamental quantities are those physical quantities that do not depend on any other physical quantity for their measurement. For example, mass, length, time, electric current, luminous intensity, temperature, and amount of substance.

Derived quantities are those physical quantities that are derived from the fundamental quantities. For example, area, volume, density, force, velocity, acceleration, linear momentum, etc.

## Measurement of Physical Quantity

The comparison of an unknown physical quantity with a known standard quantity (or constant quantity) is called measurement. In order to measure, we need two things. They are:

- The unit in which the physical quantity will measure.
- The numerical value which expresses how many times a standard quantity or unit is contained in a given physical quantity.

For example, if we measure the length of a rod, we will use a metre-scale as a standard. On measurement, if we find that the length is 5 times the standard metre scale, the length is 5 metres. In this statement, 5 is the magnitude of the length and metre is the unit of physical quantity.

## What is a Standard Unit?

The unit chosen for measuring any physical quantity is called standard unit. It has the following features:

- Standard unit should be of a suitable size.
- It should not change with respect to place and time.
- It should not change with the change in any physical conditions like temperature, pressure, volume, etc.
- It should be well defined, without any doubt or ambiguity.
- It should be easily available and accessible.
- It should be easily reproducible.

## Fundamental Units (Basic Units)

A unit which does not depend on any other unit or which can neither be changed nor related to any other fundamental unit is called fundamental unit. In simple words, the units of fundamental quantities are called fundamental units. Mass, length, time, temperature, electric current, and substance amount are the examples of fundamental quantities.. The units used to measure them are called fundamental or base units.

## Derived Units

A unit which is derived by the combination of one or more fundamental units is called derived unit. In simple words, the units of derived quantities are called derived units. For example, the unit of velocity is a derived unit.

Velocity = Displacement / Time = Length / Time

Thus, the unit of velocity can be derived in the fundamental units of length and time, i.e. m/s or ms^{-1}. Similarly, the unit of acceleration is also derived unit.

Since Acceleration = Velocity / Time = Displacement / (Time)^{2} = Length / (Time)^{2}

Thus, we can derive the unit of acceleration in the terms of fundamental units of length and time, i.e. m/s^{2} or ms^{-2}.

## System of Units

A complete set of units for both fundamental and derived physical quantities is called system of units. We commonly adopt the following system of units for measuring various physical quantities. They are as:

- CGS system
- FPS system
- MKS system
- International system of units (SI units)

**CGS System:** In this system, C stands for centimetre (length), G stands for gram (mass), and S stands for second (time). This system is in general used for smaller measurement in the terms of three basic units, such as mass, length, and time.

**FPS System:** In this system, F stands for foot (length), P stands for pound (mass), and S stands for second (time).

**MKS System:** In this system, M stands for metre (length), K stands for kilogram (mass), and S stands for second (time). MKS system is in general used for larger measurements. When the MSK system is extended to electric current, ampere (A) is taken as its fundamental unit. Then, it is called MKSA system.

## International System of Units (S.I. Units)

The system of units, which is at present internationally accepted for measurement is called an international system of units. It is abbreviated as SI units. In October 1960, the General Conference of Weights and Measures adopted SI system units. The name SI is abbreviation of the “Systeme Internationale d’ Unites” in French. In SI system, there are seven fundamental units which have shown in the below table.

### Fundamental Quantities and their SI Units

Fundamental Quantity | SI Unit | Symbol |
---|---|---|

1. Length | metre | m |

2. Mass | kilogram | kg |

3. Time | second | s |

4. Electric current | ampere | A |

5. Temperature | kelvin | K |

6. Amount of substance | mole | mol |

7. Luminous intensity | candela | cd |

In addition to these seven fundamental or base units, two more supplementary units have been included in this system. They are in the below table:

### Supplementary Quantities and their SI Units

Supplementary Quantity | SI Unit | Symbol |
---|---|---|

1. Plane angle | radian | rad |

2. Solid angle | steradian | sr |

In addition to the fundamental and supplementary units, there are a large number of derived units in this system. These derived units are expressed in terms of base units. Some examples of derived SI units expressed in terms of fundamental units are as in the below table.

### Derived Quantities and their SI Units

Derived Quantity | SI Unit | Symbol |
---|---|---|

1. Volume | cubic metre | m^{3} |

2. Area | square metre | m^{2} |

3. Speed, Velocity | metre per second | m/s or ms^{-1} |

4. Acceleration | metre per second squared | m/s^{2} or ms^{-2} |

5. Momentum | kilogram metre per second | kg m s^{-1} |

Some derived units have given special names due to their complexity while expressing in terms of fundamental units. They are as follows:

### Derived Units with Special Names

Derived Quantity | SI Unit | Symbol |
---|---|---|

1. Force | newton | N |

2. Pressure | pascal | Pa |

3. Work, Energy | joule | J |

4. Power | watt | W |

5. Frequency | hertz | Hz |

6. Electric charge | coulomb | C |

7. Electric resistance | ohm | Ω |

8. Electromotive force | volt | V |