Home | | Physics | | Physics | Dimensional Analysis

Chapter: 11th 12th std standard Class Physics sciense Higher secondary school College Notes

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Dimensional Analysis

Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised. We know that velocity = displacement / time

Dimensional Analysis

 

Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised.

 

We know that velocity   displacement / time

=  [L] / [T] = [MoL1T'1]

where [M], [L] and [T] are the dimensions of the fundamental quantities mass, length and time respectively.

 

Therefore velocity has zero dimension in mass, one dimension in length and '-dimension in time. Thus the dimensional formula for velocity is [MoL1T'1] or simply [LT'1].The dimensions of fundamental quantities are given in Table  and the dimensions of some derived quantities are given in List.

Dimensions of fundamental quantities

Fundamental quantity    Dimension

         

Length        L

Mass M

Time  T

Temperature         K

Electric current     A

Luminous intensity        cd

Amount of subtance      mol

 

Dimensional formulae of some derived quantities

 

Physical      quantity     Expression Dimensional formula

                            

Area :                   length x breadth   [L2]

Density :               mass / volume      [ML'3]

Acceleration :       velocity / time       [LT'2 ]

Momentum :         mass x velocity    [MLT'1]

Force :                  mass x acceleration        [MLT'2 ]

Work :                  force x distance    [ML2T'2 ]

Power :                 work / time [ML2T'3 ]

Energy :                Work [ML2T'2 ]

Impulse :              force  x  time        [MLT'1 ]

Radius of gyration :       Distance      [L]

Pressure :             force / area  [ML'1T'2 ]

Surface       tension :      force / length        [MT'2 ]

Frequency :          1 / time period      [T'1]

Tension :              force  [MLT'2 ]

Moment of force (or torque) : force x distance    [ML2T'2 ]

Angular      velocity :     angular displacement / time     [T'1]

Stress :                 force / area  [ML'1T'2]

Heat :                   energy         [ML2T'2 ]

Heat capacity :     heat energy/ temperature         [ML2T-2K-1]

Charge :                current x time       [AT]

Faraday constant :         Avogadro constant x     elementary charge [AT mol-1]

Magnetic induction :      force / (current x length)          [MT-2 A-1]

 

Dimensional quantities

 

Constants which possess dimensions are called dimensional constants. Planck's constant, universal gravitational constant are dimensional constants.

 

Dimensional variables are those physical quantities which possess dimensions but do not have a fixed value. Example ' velocity, force, etc.

 

Dimensionless quantities

 

There are certain quantities which do not possess dimensions. They are called dimensionless quantities. Examples are strain, angle, specific gravity, etc. They are dimensionless as they are the ratio of two quantities having the same dimensional formula.

 

Principle of homogeneity of dimensions

 

An equation is dimensionally correct if the dimensions of the various terms on either side of the equation are the same. This is called the principle of homogeneity of dimensions. This principle is based on the fact that two quantities of the same dimension only can be added up, the resulting quantity also possessing the same dimension.

 

The equation A + B = C is valid only if the dimensions of A, B and C are the same.


Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail


Copyright © 2018-2020 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.