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HOW WE CHECK DIMENSIONS CORRECTLY?

To Check the correctness of an equation.

An equation is correct only if the dimensions of each term on either side of the equation are equal. In this case the equation is dimensionally correct, but, may or may not be the correct equation for the physical quantity. If the homogeneity of dimensions does not hold good, the equation is definitely correct.

Example

Check the accuracy of the equation,

Dimension of the term S = L

Dimension of the term ut = LT ^-1 × T = L and the dimensions of the term (½)at² = LT ^-2 ×  T² = L.

Thus, we find that each term has the same dimensions. So the equation is dimensionally correct.