Dimensions
- The unit of any derived quantity depends upon one or more fundamental units. This dependence can be expressed with the help of dimensions of that derived quantity. In other words, the dimensions of a physical quantity show how its unit is related to the fundamental units.
- To express dimensions, each fundamental unit is represented by a capital letter. Thus the unit of length is denoted by L, unit of mass by M, unit of time by T, unit of electric current by I, unit of temperature by K and unit of luminous intensity by C.
- Remember that speed will always remain distance covered per unit of time, whatever be the system of units, so the complex quantity speed can be expressed in terms of length L and time T. Now, we say that dimensional formula of speed is LT-1. We can relate the physical quantities to each other (usually we express complex quantities in terms of base quantities) by a system of dimensions.
- Dimension of a physical quantity are the powers to which the fundamental quantities must be raised to represent the given physical quantity.
Illustrations
1. Find the dimension of density.
Sol. Density of a substance is defined to be the mass contained in unit volume of the substance.
Hence, [density] =[Mass]/[volume]
= M/L³
So, the dimensions of density are 1 in mass, – 3 in length and 0 in time.
Hence the dimensional formula of density is written as
[ρ]=ML^-3T^0
Important
- Constants such as ½, Π, or trigonometric functions such as “sin Αt” have no units or dimensions because they are numbers, or ratios which are also numbers.
- Two physical quantities can be equated, added (or subtracted) if and only if they have the same dimension. Why? [Verify if two quantities which have different dimensions can be multiplied (or divided) or not.
Broadly speaking, dimension is the nature of a Physical quantity. Understanding of this nature helps us in many ways.