Question

Hello users !!!

What are the applications of Dimensional analysis ?

Give a small description about those applications !!!



Units and Measurement || Physics || Class 11 CBSE ||

Answer 1

Heya......!!

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Before applications let us know about Dimensions :-

=> Whenever a derived quantity is expressed in the form of fundamental quantities that is it is written in the form of power's of the fundamental quantities to make a physical quantity is called it's Dimensions .

e.g) => Dimensions of force => [ MLT^-2 ]

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• Applications of Dimensions analysis :-

1.) => To Find the dimension of physical constant / coefficients -

=> We can write the dimensional formulae of given physical constant or coefficients by putting the formulae of given physical constant in dimensional form.

eg.) => Gravitational Constant = We can take out it's dimensional formulae by 2 formulaes.

F = Gm1m2 / r^2

g = GM / r^2

by both formulae we get the same dimensional formulae of G = [ M^-1 L^3 T^-2 ]



2.) Conversation of a physical quantity from one system to another :-

=> Basically The measures of a physical quantity is nu = constant . ( n is the numerical value is system )
we can convert from SI to CGS by some calculations .

for eg.) => Force = SI = 1 N , CGS = Dyne

=> 1 N = 10^5 Dyne.

similarly we can convert anything like 1 Joule into Erg.



3.) => To find the unit of a physical quantity.

=> If we write the formulae of any physical quantity then we can find it's Dimensions i.e Dimensional formulae by replacing it by power's of the M ,L , T .

eg.) => Work = f × s

=> MLT^-2 × L
Work = 【 M L^2 T^-2 】



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Answer 2

$<b> <i> Hello Friend!!!!☺☺$

Dimensional analysis is the use of dimensions and the dimensional formula of physical quantities to find interrelations between them.

Applications of the Dimensional Analysis

Conversion of units

The dimensions of a physical quantity are independent of the system of units used to measure the quantity in. Let us suppose that  [Math Processing Error] , [Math Processing Error] and [Math Processing Error] and [Math Processing Error] , [Math Processing Error] and [Math Processing Error]are the fundamental quantities in two different systems of units. We will measure a quantity Q (say) in both these systems of units. Suppose, a, b, c be the dimensions of the quantity respectively.

In the first system of units, Q = [Math Processing Error] [Math Processing Error] = [Math Processing Error] [ [Math Processing Error] [Math Processing Error][Math Processing Error] ]      …. (2)

In the second system of units, Q = [Math Processing Error] [Math Processing Error] = [Math Processing Error] [ [Math Processing Error] [Math Processing Error][Math Processing Error] ] …. (3)

[Math Processing Error] [[Math Processing Error] [Math Processing Error] [Math Processing Error]] = [Math Processing Error] [ [Math Processing Error] [Math Processing Error] [Math Processing Error] ]   … (4)  [using (1)]

Substitution of the respective values will give the value of [Math Processing Error] or [Math Processing Error]

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