Limitations of Dimensional Analysis

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• 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.

Solved problems

a) Convert a velocity of 48 kmh^-1 into ms^-1

b) Convert an acceleration of 48 km min^-2 into ms^-1

a) v = 48kmh^-1

1 km = 1000 m, 1h = 60 x 60 s

b) a = 48kmmin^-2

1 km = 1000 m, 1min = 60 x 60 s