Question

write the limitations of dimensional analysis as two or more physical quantity is may have some dimension ?

Answer 1

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(i) If a physical quantity depends upon more than three different base quantities, the formula cannot be derived with the help of dimensional analysis.
(ii) Dimensional analysis may not give the formula with true physical relationship, e.g., according to dimensional analysis.
s = ut + 1/2 a${{t}^{2}}$ is the correct relationship.
(iii) Dimensionless constants like 1,2,3,…, e, $\pi $ are not available in the formula derived with the help of dimensional analysis.
(iv) Formula containing trigonometric, exponential functions cannot be derived with the help of dimensional analysis.
(v) This method does not inform about the nature of the derived physical quantity, i.e., whether it is scalar or vector.

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Answer 2

Dimension-ally correct equation is sometimes incorrect because it doesn’t take into account dimensionless constants like numbers.

For e.g : v^2+2as and v^2+5as have same dimensions but they are physically incorrect.It does not test whether a physical quantity is a scalar or a vector.It cannot derive relation or formula if a physical quantity depends upon more than three factors having dimensions.It cannot derive a formula containing trigonometric function, exponential function, and logarithmic function.It cannot derive a relation having more than one part in an equation.

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