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Mention the application of dimensional equation

Last updated date: 23rd Jul 2024
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Hint: We know that dimensions are physical quantities that are expressed as the powers of the fundamental units. The dimensions are generally expressed in terms of the basic or the supplementary . These have a few significant uses as discussed below.

Complete step-by-step solution:
We know that dimensional analysis is the process of checking relations between physical quantities and their dimensions. There are seven most basic or the fundamental dimensions , namely, the mass, length, time, electric current, temperature, intensity of light and quantity of substance. And two supplementary quantities, plane angle and solid angle. Other physical quantities are derived from the basic dimensions.
There exist dimension variables, with dimensions and no fixed value. These examples include acceleration and force. There also exists dimensionless variables, these as the name suggests neither have dimensions or a fixed value. Some examples include specific gravity , coefficient of friction and refractive index to name a few.
Dimensional analysis is used to check the validity of the equations, helps in the derivation of relation between different terms and cover the units from one system to another.
However, like any system, these also have the following limitations, can not describe mathematical functions like trigonometry or logarithmic, does not throw light if the term is scalar or vector and also does describe the nature of dimensional constants.

Note: Dimensional analysis is also called the factor label method or unit factor method. This is frequently used to check the homogeneity of the term, which is expressed in an equation. An easier way of running a dimensional analysis is to compare the SI units of the terms.