IIT JEE , AIEEE Forum - Articles Category , Community shelf - Notes for Dimensional analysis {must be useful}

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Physical Quantities:
1. Primary or BasicQuantities

2. Secondary or Derived Quantities

Primary or Basic Quantities: A small group of quantities from which all other can be formed.

Example: Mass, Length, Time, Electric Current, Temperature, Luminous Intensity & Amount of Substance.

Secondary or Derived Quantities: These are the quantities which are formed with the help of primary or basic quantities.

Example: Speed, Force, Surface Tension ..............etc.

Fundamental & Derived Units

In mechanics mass, length, and time are the basic quantities. The units selected for the measurement of these quantities are called FUNDAMENTAL UNITS.

Those quantities which are formed the fundamental units are called DERIVED UNITS.

Dimensions

Dimension of a derived unit are the powers to which the fundamental units of mass, length, time, etc. must be raised to represent the unit.

Dimensional Formula

Dimensional formula is an expression which shows how & which of the fundamental units are required to represent the unit of a physical quantity.

Dimensional Equation

Dimensional equation is the equation obtained by equating the physical quantity with its dimensional formula.

4 Categories of Physical Quantities

1) Dimensional Constants: Physical quantities which posses dimensions and have a fixed value.

2) Dimensional Variables: Physical quantities that posses dimensions and do not have a fixed value.

3) Dimensionless Constants: Physical quantities which do not posses dimensions and have a fixed value.

4) Dimensionless Variables: Physical quantities which do not posses dimensions and do not have a fixed value.

Principal of Homogeneity of Dimensions

A given physical relation is dimensionally correct if the dimensions of the various terms on either side of the relation are the same.

Use of Dimensional Equation

- To convert a physical quantity from one system to another.

N1U1=N2U2

- To check the dimensional correctness of a given physical relation.

- To establish a relation between different physical quantity.

Limitations of Dimensional Analysis

# Supplies no information about dimensionless constants. They have to be determined by experiment or mathematical investigation.

# This method is applicable only in case of power functions. It fails in case of exponential and trigonometric relations.

# This method fails to derive directly a relation which contains two or more quantities of like nature.

# It fails to derive the exact form of a physical relation, if a physical quantity depends upon more than three other physical quantities.

# If we cannot identify all factors on which a physical quantity depends, then the method of dimensional analysis cannot be used to derive expression for a physical quantity.

# It can only check whether a physical relation is correct or not. It cannot tell whether the relation is absolutely correct or not.

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