Physics > Unit and Dimensions > 11.0 Application of dimensional analysis
Unit and Dimensions
1.0 Introduction
2.0 Physical quantity
3.0 SI units
3.1 Definition of standard units
3.2 System of units
3.3 Rules for writing units
3.4 Characteristics of a standard unit
3.5 Advantages of SI
4.0 SI prefixes
5.0 Conversion of units
6.0 Important practical units
7.0 Dimensions
8.0 Dimensional formula
9.0 Dimensional equation
10.0 List of dimensional formula
11.0 Application of dimensional analysis
11.1 To check the dimensional consistency of equations
11.2 To deduce relation among the physical quantities
11.3 To convert one system of unit into another system of unit
12.0 Limitations of dimensional analysis
11.3 To convert one system of unit into another system of unit
3.2 System of units
3.3 Rules for writing units
3.4 Characteristics of a standard unit
3.5 Advantages of SI
11.2 To deduce relation among the physical quantities
11.3 To convert one system of unit into another system of unit
For this, we use the relation,
$${n_2} = {n_1}{\left( {\frac{{{M_1}}}{{{M_2}}}} \right)^a}{\left( {\frac{{{L_1}}}{{{L_2}}}} \right)^b}{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^c}$$
where
$M_1$, $L_1$, $T_1$ are fundamental units on one system.
$M_2$, $L_2$, $T_2$ are fundamental units on other system.
$a,b,c$ are the dimensions of the quantity in mass, length and time respectively.
$n_1$ is the numerical value in one system.
$n_2$ is the numerical value in another system.
Note: This formula is valid only for absolute units and not for gravitational units.
