The method of dimensions has the the following limitations:
1.It does not help us to find the value of dimensionless constants involved in various physical relations.The value,of such constant have to be determined by some experiments or mathematical investigations.
2.This method fails to derive formula of a physical quantity which depends upon more than three factors.Because only three equations are obtained by comparing the powers of M,L and T and it is not possible to find more than three variables by solving three equations.
However,in S.I.units formulas for physical quantities depending upon more than three quantities can be derived because there are seven base units.
3.This method is applicable only in case of power functions.It fails to derive relations of quantities involving exponential and trigonometric functions.
4.The method connot be directly applied to derive relations which contain more than one terms on one side or both sides of the equation,such as v = u+ at or S = ut + 1/2 at2 etc.However,such relations can be derived indirectly.
5.A dimensionally correct relation may not be true physical relation because the dimensional equality is not sufficient for telling the correctness of a given physical relation.
e.g.,v = u -100 at and (v = 5u + 20at) are dimensionally true but actually are in correct.
6.This method gives us no information,whether a physical quantity is a scalar quantity or a vector quantity.
7.This method fails to drive a relation which contains two or more variables with same dimensions.
1.It does not help us to find the value of dimensionless constants involved in various physical relations.The value,of such constant have to be determined by some experiments or mathematical investigations.
2.This method fails to derive formula of a physical quantity which depends upon more than three factors.Because only three equations are obtained by comparing the powers of M,L and T and it is not possible to find more than three variables by solving three equations.
However,in S.I.units formulas for physical quantities depending upon more than three quantities can be derived because there are seven base units.
3.This method is applicable only in case of power functions.It fails to derive relations of quantities involving exponential and trigonometric functions.
4.The method connot be directly applied to derive relations which contain more than one terms on one side or both sides of the equation,such as v = u+ at or S = ut + 1/2 at2 etc.However,such relations can be derived indirectly.
5.A dimensionally correct relation may not be true physical relation because the dimensional equality is not sufficient for telling the correctness of a given physical relation.
e.g.,v = u -100 at and (v = 5u + 20at) are dimensionally true but actually are in correct.
6.This method gives us no information,whether a physical quantity is a scalar quantity or a vector quantity.
7.This method fails to drive a relation which contains two or more variables with same dimensions.