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Unit and Dimension 

Any physical quantity requires a numerical value and a standard or scale for its quantitative representation. The standard or the scale by which the physical quantity is represented is known as the UNIT.

All physical quantities do not have unit, quantities which are represented as the ration of the two same physical quantities do not have any unit.

Example: Refractive Index (μ) =velocity of light in vacuum/velocity of light in medium

Specific Gravity = Density of the substance/density of water

Generally we have three fundamental physical quantities

1. Mass

2. Length

3. Time

They are called fundamental because they do not require the help of other physical quantity for their representation.

Most of the other physical quantities can be represented in terms of these physical quantities. When a physical quantity is represented in terms of fundamental quantities it is known as dimension of that physical quantity.

  Units: Generally we have two types of units

1. Fundamental Unit

2. Derived Unit

Fundamental Unit: The units of fundamental quantities are known as fundamental units.

Derived Unit: The units of all other physical quantities which can be derived from the fundamental units are known as derived units.

System of Units: We have the following system of fundamental units

Sr No.





































Angle: Radian, Solid Angle : Ste-Radian, Temperature : Kelvin, Luminous Intensity: Candela

The MKSA was un-rational system later MKSA was rationalised by introducing special constant and is known as International System of Unit (SI unit).

The seven fundamental units are:

  • meter(m), is the length of the path traveled by light in vacuum in an interval of 1/299 792 458 seconds;
  • second(s), is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium 133;
  • kilogram(kg), is the unit of mass; it equal to the mass of the international prototype of the kilogram. This prototype, made ​​of platinum-iridium, is kept at Sevres in 1889;
  • ampere(A), is the intensity of a constant electric current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, placed at a distance of one meter in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length;
  • kelvin(K), unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water;
  • mole(mol), is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of carbon 12. When the mole is used, the elementary entities must be specified; may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles;
  • candela(cd), is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and intensity in that direction of 1/683 watt per steradian.



Derived Unit: To find derived unit of a physical quantity we must write the dimension of that physical quantity.



               Unit: CGS = cm sec-1

               SI=m sec-1




              Unit: CGS = cm sec-2

               SI=m sec-2




              Unit: CGS = gm.cm. sec-2 = 1 dyne

               SI=kg.m. sec-2 = 1 Newton




              Unit: CGS = gm.cm2. sec-2 = 1 erg

               SI=kg.m2. sec-2 = 1 Joule


5.       )


Unit: CGS=gmcm-1Sec-1 = ( 1 Poise )

SI: Kg m-1S-1



Use of Dimension

A.      From the dimension of physical quantity we can convert from one system of unit to other.

1.        Example: Dyne and Newton both are units of force one in C.G.S and other is in SI respectively                   find 1 Dyne = ? Newton


We know 


In C.G.S    1 Dyne = 1 gm.1cm.1sec-2


1 Dyne = 10-3 Kg.10-2m.1 sec-2

1 Dyne = 10-5 Newton


1         Newton = 105 Dyne


2.       Both Erg and Joule are units of Work find 1 Erg  = ? Joule

       We know 

               In CGS = gm.cm2. sec-2 = 1 erg

               SI=kg.m2. sec-2 = 1 Joule

               1 Erg = 1gm.cm2. sec-2

               1 Erg = 10-3Kg.(10-2)2m2. sec-2

               1 Erg = 10-7 Joule

1         Joule = 10-7 Erg



3.       Vlaue of G = 6.667 X  10-8 CGS Unit. Find the value in S.I Unit


We Know that [G]

In C.G.S            G = 6.667 X 10-8 gm-1 cm3 sec-2 


                          G = 6.667 X 10-8(10-3)-1 Kg-1 (10-2)3m3 sec-2 


                          G = 6.667 X 10-11 S.I unit




B.      By writing dimension we can check whether the given equation is correct or not?

Dimension of L.H.S = [T]

Dimension of R.H.S =     =  [T]

We found that the dimension of both sides of this equation is same hence above equation is dimensionally correct.


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