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Units and Measurements — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements3 Marks
Question
A dimensionally correct equation need not actually be a correct equation but dimensionally incorrect equation is necessarily wrong. Justify.
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Answer

$i)$ To justify a dimensionally correct equation need not be actually a correct equation, consider equation, $v^2 = 2as$
Dimensions of $\text{L.H.S.} = [v^2] = [L^2M^0T^2]$
Dimensions of $\text{R.H.S.}= [as]= [L^2M^0T^2]$
$\rightarrow \text{[L.H.S.] = [R.H.S.]}$
This implies equation $v^2 = 2as$ is dimensionally correct.
But actual equation is, $v^2 = u^2 + 2as$
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 $\text{L.H.S.} = [mv] = [L^1M^1T^{-1}]$
Dimensions of $\text{R.H.S.} = [mgh] = [L^2M^1T^{-2}]$
Since the dimensions of $\text{R.H.S.}$ and $\text{L.H.S.}$ are not equal, the formula given by equation must be incorrect.
This confirms dimensionally incorrect equation is necessarily wrong.

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