Question

State any two limitations of dimensional analysis.

Answer 1

Hint: The investigation of the connection between physical amounts with the assistance of measurements and units of estimation is named as dimensional analysis. Dimensional analysis is basic since it keeps the units the equivalent, helping us perform numerical figuring easily.

Complete answer:
Dimensional analysis is also called factor label method or unit analysis which is further used to convert the one set of units to another set. This method is used for both simple (feet to inches) and complex (\[g/c{{m}^{3}}\] to \[\dfrac{kg}{gallon}\]) conversions and uses the relationships or conversion factors between the different sets of the units.
(i). The value of dimensionless constants cannot be determined by this method.
(ii). This method cannot be applied to equations involving exponential and trigonometric functions.
(iii) It cannot be applied to an equation involving more than three physical quantities.
Example: \[F\text{ }=\text{ }\left[ M \right]\text{ }\times \text{ }[{{L}^{1}}~{{T}^{-}}^{2}]\text{ }=\text{ }{{M}^{1}}~{{L}^{1}}~{{T}^{-}}^{2}\].Force is dimensionally represented as\[{{M}^{1}}~{{L}^{1}}~{{T}^{-}}^{2}\].

Note:
Significance of dimensional analysis: -
1.The definition itself implies its significance for example we can improve any complex physical amount into essential things which in turns turn out to be simple for us to see, how the amount is communicated, how is its recipe inferred and how to see the connection between the amounts which are utilized to communicate them.
2. It is one of the best valuable apparatuses accessible which encourages doing unimaginable scientific issues become simpler to illuminate. By one way or another it is additionally called “open polynomial math".
3. It diminishes the quantity of cases to be considered to take care of an issue by lessening its greater multifaceted nature.