Fundamental and Derived Units

**Category : **11th Class

Normally each physical quantity requires a unit or standard for its specification so it appears that there must be as many units as there are physical quantities. However, it is not so. It has been found that if in mechanics we choose arbitrarily units of any three physical quantities we can express the units of all other physical quantities in mechanics in terms of these. Arbitrarily the physical quantities mass, length and time are chosen for this purpose. So any unit of mass, length and time in mechanics is called a fundamental, absolute or base unit. Other units which can be expressed in terms of fundamental units, are called derived units. For example light year or km is a fundamental unit as it is a unit of length while s^{-1}, m^{2 }or kg/m are derived units as these are derived from units of time, mass and length.

**System of units :** A complete set of units, both fundamental and derived for all kinds of physical quantities is called system of units. The common systems are given below

**(1) CGS system :** This system is also called Gaussian system of units. In this length, mass and time have been chosen as the fundamental quantities and corresponding fundamental units are centimetre (cm), gram (g) and second (s) respectively.

**(2) MKS system :** This system is also called Giorgi system. In this system also length, mass and time have been taken as fundamental quantities, and the corresponding fundamental units are metre, kilogram and second.

**(3) FPS system :** In this system foot, pound and second are used respectively for measurements of length, mass and time. In this system force is a derived quantity with unit poundal.

**(4) S. I. system :** It is known as International system of units, and is extended system of units applied to whole physics. There are seven fundamental quantities in this system. These quantities and their units are given in the following table Unit and symbol of quantities

Quantity |
Unit |
Symbol |

Length | metre | m |

Mass | kilogram | kg |

Time | second | s |

Electric Current | ampere | A |

Temperature | Kelvin | K |

Amount of Substance | mole | mol |

Luminous Intensity | candela | cd |

Besides the above seven fundamental units two supplementary units are also defined ? Radian (rad) for plane angle and Steradian (sr) for solid angle.

**Note :**

- Apart from fundamental and derived units we also use practical units very frequently. These may be fundamental or derived units e.g., light year is a practical unit (fundamental) of distance while horse power is a practical unit (derived) of power.
- Practical units may or may not belong to a system but can be expressed in any system of units e.g., 1 mile = 1.6 km = 1.6 × 10
^{3}m.

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