Question

Sir what is meant by dimensional analysis and its limitations .
Can I have a answer in easy language. Not understood any of the dimensional analysis ?

Answer 1

The study of relationships between physical quantities with the help of their dimensions and units of measurements is called dimensional analysis.

We use dimensional analysis in order to convert a unit from one form to another. In science and mathematical problems, we have to keep the unit same so that we can perform the mathematical operations easily.

Dimensional Analysis is also called Factor Label Method or Unit Factor Method as we use conversion factor in order to get same units. As an example, if we want to know how many minutes are in 3 hours, what do we do? We generally think as follows:

1 hour = 60 minutes

3 hour = 3 × 60 minutes = 180 minutes

(here the conversion factor 60 minutes)

We use conversion factors accordingly so that the answer comes in the desired unit and biased results are avoided.

Limitations of Dimensional Analysis

• Dimensional analysis has no information on dimensionless constants.

• If a quantity is dependent on trigonometric or exponential functions, this method cannot be used.

• In some cases, it is difficult to guess the factors while deriving the relation connecting two or more physical quantities.

• This method cannot be used in an equation containing two or more variables with same dimensions.

• It cannot be used if the physical quantity is dependent on more than three unknown variables.

• This method cannot be used if the physical quantity contains more than one term, say sum or difference of two terms.