Dimensional Formula and Dimensional Equation
Dimensional Formula is the expression which shows how and which of the base quantities represent the dimensions of a physical quantity.
Dimensional Equation is an equation obtained by equating a physical quantity with its dimensional formula.
Physical Quantity
Dimensional Formula
Dimensional Equation
Volume [ M 0 L 3 T 0 ] [ V ] = [ M 0 L 3 T 0 ]
Speed [ M 0 L T-1 ] [ υ ] = [ M 0 L T-1 ]
Force [ M L T-2 ] [ F ] = [ M L T-2 ]
Mass Density [ M L-3 T 0 ] [ ρ ] = [ M L-3 T 0 ]
Dimensional Analysis
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Only those physical quantities which have same dimensions can be added and subtracted. This is called principle of homogeneity of dimensions.
Dimensions can be multiplied and cancelled like normal algebraic methods.
In mathematical equations, quantities on both sides must always have same dimensions.
Arguments of special functions like trigonometric, logarithmic and ratio of similar physical quantities are dimensionless.
o Equations are uncertain to the extent of dimensionless quantities.
Example Distance = Speed x Time. In Dimension terms, [ L ] = [ LT-1 ] x [ T ]
Since, dimensions can be cancelled like algebra, dimension [ T ] gets cancelled and the equation becomes [ L ] = [ L ].