A dimensionally correct equation need not actually be a correct equati

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

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

Answer»

(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.