How To Write A Dimensional Formula? (Class 11)

In order to make the measurement of a physical quantity we have, first of all, to evolve a standard for that measurement so that different measurements of same physical quantity can be expressed relative to each other. That standard is called a unit of that physical quantity.

System of Units:
(a) C.G.S (Centimeter-Grand-Second) system.
(b) F.P.S. (Foot-Pound-Second) system.
(c) M.K.S. (Meter-Kilogram--Second) system.
(d) M.K.S.A. (Meter-Kilogram-Second-Ampere) unit.

Dimensional Formula:

Dimensional formula of a physical quantity is the formula which tells us how and which of the fundamental units have been used for the measurement of that quantity.

How to write dimensions of physical quantities:
(a) Write the formula for that quantity, with the quantity on L.H.S. of the equation.
(b) Convert all the quantities on R.H.S. into the fundamental quantities mass, length and time.
(c) Substitute M, L and T for mass, length and time respectively.
(d) Collect terms of M,L and T and find their resultant powers (a,b,c) which give the dimensions of the quantity in mass, length and time respectively.

Characteristics of Dimensions:
(a) Dimensions of a physical quantity are independent of the system of units.
(b) Quantities having similar dimensions can be added to or
subtracted from each other.
(c) Dimensions of a physical quantity can be obtained from its units and vice-versa.
(d) Two different physical quantities may have same dimensions.
(e) Multiplication/division of dimensions of two physical quantities (may be same or different) results in production of dimensions of a third quantity.