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E-STAR - Student
E-Lecture - Dimensional Analysis and its use in Physics

The dimension of a physical quantity refers to the fundamental units contained in it. Any quantity which can be measured in length units, are said to have the dimension of length (L). Any quantity which can be measured in mass units is said to have the dimensions of mass (M). Similarly any quantity which can be measured in time units have the dimension of time (T). The dimension of a quantity is written in square bracket as follows. [mass] = M, [length] = L, and [time] = T,where the square brackets mean “the dimension of the quantity within”.

The derived units are based on the fundamental units and in many cases involve more than one fundamental unit. The dimension of derived quantities are expressed in general as MxLyTz. Here x, y, and z indicate the number of times the unit of the particular fundamental physical quantity is involved.