Dimensional Quantities, Dimensionless Quantities, Principle of Homogeneity

On the basis of dimension, we can classify quantities into four categories.

(1)Dimensional variables

Physical quantities, which possess dimensions and have variable values are called dimensional variables. Examples are length, velocity, and acceleration etc.

(2) Dimensionless variables

Physical quantities which have no dimensions, but have variable values are called dimensionless variables. Examples are specific gravity, strain, refractive index etc.

(3) Dimensional Constant

Physical quantities which possess dimensions and have constant values are called dimensional constants. Examples are Gravitational constant, Planck’s constant etc.

(4) Dimensionless Constant

Quantities which have constant values and also have no dimensions are called dimensionless constants. Examples are π, e (Euler’s number), numbers etc.

Principle of homogeneity of dimensions

The principle of homogeneity of dimensions states that the dimensions of all the terms in a physical expression should be the same. For example, in the physical expression \(v^2\) = \(u^2\) + 2as, the dimensions of \(v^2\), \(u^2\) and 2 as are the same and equal to [\(L^2T^{−2}\)].