## Unit – I B |

## System of Units – Units and Measurements

- A system of units is collection of units in which certain units are chosen as fundamental and all other are derived from them. This system is also called as absolute system of units.
- In most of the system the mass, the length and the time are considered to be fundamental quantities and their units are called as fundamental units.
- Following are some systems of units which are in common use.
#### c.g.s. system of units

Unit of length is centimetre (cm). Unit of mass is gram (gm). Unit of time is second (s)

#### m.k.s. system of units

Unit of length is metre (m). Unit of mass is kilogram (kg). Unit of time is second (s)

#### f.p.s. system of units

Unit of length is foot (ft). Unit of mass is pound (Lb). Unit of time is second (s)

### S.I. system of units:

- In October 1971 a replacement of metric system of units was done with a new system called Systeme Internationale d’Unites
- This system of units is improvement and extension of the traditional metric system. Now this system of units has replaced all other systems of units in all branches of science, engineering, industry and technology.

#### Advantages of S.I. System of Units:

- Units are simple to express.
- SI system is coherent system of units. Coherent system of units is one in which derived units are obtained by multiplying or dividing the fundamental units, without introducing any multiplying factor.
- Units of many physical quantities are related with each other through simple and elementary relationships

For examples 1 ampere = 1 volt / 1 ohm. - There is decimal relationship between the units of same quantity and hence it is possible to express any small or large quantity as a power of 10. i.e. inter-conversion is very easy.

For e.g. 1kg = 1000 gm = 10^{3}gm - The physical quantities can be expressed in terms of suitable prefixes.
- joule is unit of all forms of energy and it is a unit of work. Hence it forms link between mechanical and electrical units.
- This system forms logical and interconnected framework for all measurements in science, technology and commerce.
- All derived units can be obtained by dividing and multiplyingthe basic and supplementary units and no numerical factors are introduced as in other system of units. Hence S.I. systm of units is coherent system. Hence S.I. system of units is used worldwide.

### Units outside SI but Frequently Used in Physics:

Name | Symbol | Value in SI units |

minute (time) | min | 1 min = 60 s |

hour | h | 1 h = 60 min = 3600 s |

day | d | 1 d = 24 h = 86 400 s |

degree (angle) | ° | 1° = ( /180) rad |

minute (angle) | 1 = (1/60)° = (/10 800) rad | |

second (angle) | 1 = (1/60) = (/648 000) rad | |

liter | L | 1 L = 1 dm^{3 }= 10^{-3} m^{3} |

metric ton ^{(a)} | t | 1 t = 10^{3} kg |

neper | Np | 1 Np = 1 |

bel^{ (b)} | B | 1 B = (1/2) ln 10 Np ^{(c)} |

electronvolt ^{(d)} | eV | 1 eV = 1.602 18 x 10^{-19} J, approximately |

unified atomic mass unit^{ (e)} | u | 1 u = 1.660 54 x 10^{-27} kg, approximately |

astronomical unit^{ (f)} | ua | 1 ua = 1.495 98 x 10^{11} m, approximately |

**Units Currently Accepted for Use with the SI System:**

Name | Symbol | Value in SI units |

nautical mile | 1 nautical mile = 1852 m | |

knot | 1 nautical mile per hour = (1852/3600) m/s | |

are | a | 1 a = 1 dam^{2} = 10^{2} m^{2} |

hectare | ha | 1 ha = 1 hm^{2 }= 10^{4} m^{2} |

bar | bar | 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 10^{5} Pa |

ångström | Å | 1 Å = 0.1 nm = 10^{-10} m |

barn | b | 1 b = 100 fm^{2} = 10^{-28} m^{2} |

curie | Ci | 1 Ci = 3.7 x 10^{10} Bq |

roentgen | R | 1 R = 2.58 x 10^{-4} C/kg |

rad | rad | 1 rad = 1 cGy = 10^{-2} Gy |

rem | rem | 1 rem = 1 cSv = 10^{-2} Sv |