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Limitation of Dimensional Analysis, i), , The value of dimensionless constant can be obtained with, the help of experiments only., ii) Dimensional analysis cannot be used to derive relation, involving trigonometric, exponential and logarithmic, function as these quantities are dimensionless., iii) Dimension analysis is not useful if constant of, proportionality is not a dimensionless quantity., e.g. Gravitational force between two point masses is, directly proportional to product of the two masses and, inversely proportional to square of the distance between, the two., 𝑚 𝑚, 𝐹 𝛼 12 2, 𝑟, 𝑚1 𝑚2, 𝑙𝑒𝑡 𝐹 = 𝐺, 𝑟2, The constant of proportionality ‘G’ is NOT dimensionless., Thus earlier method will not work., iv) If the correct equation contains some more terms of the, same dimension, it is not possible to know about their, presence using dimensional equation., 1, ∙However, the complete equation is 𝑆 = 𝑢𝑡+ 𝑎𝑡 2, 2, , Error :, The difference between the true value and measured value of a, physical quantity is called error., Error may be positive or negative., The true value of physical quantity can never be known.