###### Chapter Content :

**Physical Quantity**

**A physical quantity is a quantity that can be measured i.e. a physical quantity is properly defined, has proper units, and its value can be measured by an instrument.**

**Physical quantities are classified as fundamental and derived quantities.**

**Fundamental Quantities **

**Fundamental quantities are those that are defined directly by the process of measurement only. They are not defined in terms of other quantities; their units are not defined in terms of other units. In mechanics we treat length, mass and time as basic or fundamental quantities.**

**Derived Units**

**The units of all other physical quantities, which can be obtained from fundamental units, are called derived unit.**

System of units |
Length |
Mass |
Time |

F.P.S |
Foot |
pound |
second |

C.G.S |
centimeter |
gram |
second |

M.K.S(S.I) |
meter |
kilogram |
second |

**Illustration : Find the unit of speed.**

**Solution :**

__Definitions of Base Units:__

__Definitions of Base Units:__** Meter:**

**Since 1983, the standard metre is defined as the length of the path travelled by light in vacuum in (1/299,792,458) th part of a second.**

** Kilogram:**

**Nowadays the standard kilogram is the mass of a cylinder made of platinum-iridium alloy and stored in a special vaule in the International Bureau of Weights and Measures at Sevres in France.**

**Second:**

**At present second is defined on the basis of an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom. When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to other. One second is defined as the time required for 9,192,631,770 cycles of this radiation**

**In physics SI system is based on seven fundamental and two derived units.**

Basic Physical Quantities: |
Fundamental Unit: |

Mass |
kilogram |

Length |
meter |

Time |
second |

Temperature |
kelvin |

Electric current |
ampere |

Luminous intensity |
candela |

Quantity of matter |
mole |

Supplementary Physical Quantities |
Supplementary unit |

Plane angle |
radian |

Solid angle |
steradian |

**Some Practical units:**

**Some Practical units:**

**For the measurement of very large distance, the following three units are used.**

**(i) Astronomical Unit (AU) : It is the average distance of the centre of the sun from the centre of the earth.**

**1 AU = 1.5 × 10 ^{11 }metre**

**(ii) Light year : It is defined as the distance traveled by light in vaccum in one year**

**1 light year = 3 × 10 ^{8} × (365 × 24 × 60 × 60) metre**

**1 ly = 9.4 × 10 ^{15 }metre**

**(iii) Par sec : It is defined as the distance at which an are 1 AU long subtends an angle of 1’’**

**1 par sec = 3.1 × 10 ^{16 }metre**

**Illustration : Fill in the blank by suitable conversion of units**

**1 kg m ^{2}s^{-2} =….. g cm^{2}s^{-2}**

**Solution : 1kg m ^{2}s^{-2} = 1×10^{3} g (10^{2}cm)^{2 }s^{-2}**

**= 10 ^{7}g cm^{2 }s^{-2}**

**Exercise 1: (i) What is the value of one micron in centimeter ?**

**(ii) What is the value of a pressure of 10 ^{6} dynes/cm^{2} in S.I unit ?**

**Exercise 2:Fill in the blanks :**

**(a) The volume of a cube of side 1 cm is equal to …..m ^{3}**

**(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to …….(mm)**^{2}

**(c) A vehicle moving with a speed of 18 km/h covers………m in 1 s**

**(d) The relative density of lead is 11.3. Its density is …….g cm**^{3}or ……..kg m^{3}.**Exercise 3: Fill in the blanks by suitable conversion of units :**

**(a) 1 kg m ^{2} s^{2} = ….g cm^{2} s^{2}**

**(b) 1 m = ….. ly**

**(c) 3.0 m s**^{-2}= …. km h^{-2}

**(d) G = 6.67 × 10**^{-11}N m^{2}(kg)^{-2}= …. (cm)^{ 3}s^{-2}g^{-1}**Exercise 4: A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m ^{2} s^{-2}.**

**Suppose we employ a system of units in which the unit of mass equals α kg , the unit of length equals β m , the unit of time is γ s. Show that a calorie has a magnitude 4.2 α**^{-1}β^{-2}γ^{2}in terms of the new units.