A dimensionally correct equation need not actually be a correct equation but dimensionally incorrect equation is necessarily wrong. Justify.

Monjur Alahi

A dimensionally correct equation need not actually be a correct equation but dimensionally incorrect equation is necessarily wrong. Justify.


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Salim Ahmed Kawsar

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(i) To justify a dimensionally correct equation need not be actually a correct equation,

consider equation, v2 = 2as

Dimensions of L.H.S. = [v2] = [L2M0T2]

Dimensions of R.H.S. = [as]= [L2M0T2]

⇒ [L.H.S.] = [R.H.S.]

This implies equation v2 = 2as is dimensionally correct.

But actual equation is, v2 = u2 + 2as

This confirms a dimensionally correct equation need not be actually a correct equation.

(ii) To justify dimensionally incorrect equation is necessarily wrong, consider the formula, \(\frac{1}{2}\) mv = mgh

Dimensions of L.H.S. = [mv] = [L1M1T-1]

Dimensions of R.H.S. = [mgh] = [L2M1T-2]

Since the dimensions of R.H.S. and L.H.S. are not equal, the formula given by equation must be incorrect.

This confirms dimensionally incorrect equation is necessarily wrong.

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