Dimensional analysis is a method used to check the correctness of the equation and simplify complex equations. This article covers what is dimensional analysis, the application of dimensional analysis, uses of dimensional analysis, what is principle of homogeneity of dimensions, limitations of dimensional analysis
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The principle of homogeneity of dimensions says that “ In any physical mathematical equation the dimensions of each term appearing in the equation are the same on each side of that equation”. This is called the principle of homogeneity.
In physics, any physical quantity can be expressed in terms of fundamental units, and the representation of a physical quantity in terms of fundamental units is called the dimension of the physical quantity.
Following are the symbols for fundamental units used in Dimensional Analysis class 11.
Name of the Unit | Symbol |
Length | [L] |
Time | [T] |
Mass | [M] |
Electric current | [A] |
Temperature | [K] |
Amount of substance | [mol] |
Intensity of light | [cd] |
When we represent each physical quantity of a mathematical equation in its dimensional form then analysis of dimensions to determine whether a given equation is correct or not dimensionally is known as dimensional analysis.
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Application of dimensional analysis in various fields are:
The most widely uses of dimensional analysis are mentioned as:
When we analyze the physical equation by using their dimensions such as Distance, velocity, and Time relation.
We know that the Dimension of physical quantity Velocity is
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Some of the limitations of dimensional analysis are:
1. Check the correctness of the equation
We will use the dimensional analysis and principle of homogeneity which can be used If the dimension of quantity ‘
The force has a dimension of mass×acceleration so, the dimension of ‘
Now, the dimension of radius which is simply the distance will be the Dimension of
Hence, the dimension of quantity f is the Dimension of force
2. Check the correctness of the equation
We will use the dimensional analysis and principle of homogeneity which can be used If the dimension of quantity
Now, let us find the dimension of quantity 2aS as 2 is a dimensionless constant, and the multiplication of
3. Dimensional analysis of
We will do the Dimensional analysis of
(A) Force F
(B) Velocity V
(C) Planck Constant h
(D) Mass M
A dimensional constant is a constant quantity in physics that has a constant numerical value and has proper dimensions. Force is not a constant quantity as it depends upon mass and velocity is also not a constant quantity as it depends upon distance and time similarly mass can have any numerical value but Plank constant h has a fixed value of h=6.62×10-34Js. and Planck constant has also a fixed dimension of [ML2T-1] Hence, (C) Planck Constant h is a dimensional constant.
In physics, Dimensional analysis is a method of checking the validity and as well as finding the dimensions of any physical term in a mathematical equation consisting of physical parameters using the principle of homogeneity and dimensions of physical quantities is known as Dimensional analysis.
The principle of homogeneity of dimensions states that, If we have a physical mathematical equation then the dimensions of each term in the left side of the equation and dimension of each term in the right side of the equation will always be the same. This principle is known as the principle of homogeneity in dimensions.
In physics, every physical quantity can be expressed in terms of the fundamental units needed to represent it completely; the representation of a physical quantity with the fundamental units is known as the dimension of that physical quantity.
Two most important uses of dimensional analysis is mentioned as:
Dimensional analysis uses the principle of homogeneity which enables us to check the correctness of any physical mathematical equation.
Dimensional analysis method is also used to convert one system of units to another system of unit by comparing the dimensions of a physical quantity in each units system respectively.
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