What is dimensional consistency - Definition and Meaning

Dimensional Consistency :

If the dimension of the quantities are equal on both sides of the equation, then it is said to be dimensionally consistent.


Example :

Consider the equation of pendulum T= 2 Pi * sqrt(L/g) Dimension of length->L , Time-> T value of g= 9.8 ms-2 , in dimension LT -2 (omitting constant values) Take RHS : = √(L/LT -2) = √(1/T -2) = √(T2) = T = LHS It shows the equation is Dimensionally consistent.
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