Table of Contents

**Fundamental Units and Derived Units**

Physical quantities can be divided into two categories – base quantities and derived quantities. The units for these quantities are called fundamental units and derived units.

**Fundamental units:** *Physical quantities which are independent and cannot be derived from other physical quantities are called fundamental quantities *and their units are called the fundamental or base units. The fundamental physical quantities are mass, time, length, temperature, electric current, intensity of light and quantity of matter.

**Derived Units: **The units of physical quantities which can be expressed in terms of fundamental units are called derived units. Units of speed, force, momentum etc. are derived units.

**Characters of a Standard Unit**

Standard unit of physical quantity must have following characteristics:

- It should be defined.
- It should remain constant.
- It should be easily available and reproducible.
- It should be universally agreed.

**System of Units**

Different systems of units are used in measurement. For example, MKS system, CGS-system, FPS system SI-units is mostly used in measurement in science and engineering.

**MKS-system: **In this system, unit of length is metre, unit of mass is kilogram and unit of time is second.

**CGS-system:** In this system, length is measured in centimetre, mass in gram and time in second.

**FPS-system: **In this system, length is measured in foot, mass in pound and time in second.

**SI-units: **In this system, seven basic and two supplementary units are taken. Length is taken in metre, mass in kilogram, time in second, temperature in Kelvin, electric current in ampere, luminous intensity in candela and quantity of matter in mole.

Two supplementary units are plane angle and solid angle, and their units are radian and steradian respectively.

The fundamental quantities adopted by the SI-units, their units and symbols are given in the following table:

**Units of Fundamental Quantities**

Fundamental Quantity | Unit | Symbol |

Length | metre | m |

Length | kilogram | kg |

Time | second | s |

Temperature | Kelvin | k |

Current | ampere | A |

Luminous intensity | candela | cd |

Amount of Substance | mole | mol |

In addition to the above seven fundamental units in SI-units, two supplementary units are also defined. These supplementary units are given in the table below.

**Supplementary Units**

Quantity | Unit | Symbol |

Plan angle | radian | rad |

Solid angle | steradian | sr |

**Definitions of SI Base Units**

**Metre: ***The metre is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.*

**Second: ***The second is the duration of 9,162,631,770 periods of the transition between the two hyperfine levels of the ground state of the cesium-133 atoms.*

**Kilogram: ***The Kilogram is the mass equal to the mass of standard platinum-iridium alloy cylinder (90% platinum and 10% iridium) kept at the International Bureau of Weights and Measures in pairs. *This cylinder is about 4 cm high in diameter.

**Advantages of SI-Units**

The SI-unit has a number of advantages.

- It is a rational system of units.
- It is a coherent system of units.
- It is a decimal system.
- It is highly useful in practical and theoretical work.

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Fundamental Units and Derived Units