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 ].