Dimension of a physical quantity is a function that determines the number of times we need to alter the numerical value of physical quantity while passing from one system of units of measurement to the another system of units of measurement within the same class.
Dimensional quantity:
A dimensional quantity is one whose numerical value is changed upon transition from one system of units of measurement to another system of units of measurement within the same class.
Consider a physical quantity, Force, and say in MKS system,
The value of Force is F = 9N = 9kgms-2
So, F = 9kgms-2
We want to make a transition from MKS to CGS units of measurement.
While passing from MKS to CGS units of measurement,
The unit of mass is decreased by a factor, M = 1000
The unit of length is decreased by a factor, L = 1000
The unit of time is decreased by a factor, T = 1000
We know the dimension of force is [F] = MLT-2
So, According to the definition of dimension, the numerical value of force in CGS unit will be
F = 9 x MLT-2 gcms-2
= 9 x 1000 x 100 x 1-2 gcms-2
= 9 x 105 gcms-2
So, in transition from MKS to CGS unit-
The numerical value of force is increased by a factor MLT-2
And the unit of force is decreased by a factor MLT-2
So, Force is a dimensional quantity with dimension [MLT-2]
