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  4. If force is proportional to square of velocity, then the dimensions of proportionality constant is

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Q. If force is proportional to square of velocity, then the dimensions of proportionality constant is

ManipalManipal 2010Physical World, Units and Measurements

Solution:

As $F \propto v^{2}$
or $F=k v^{2}$
$\therefore k=\frac{F}{v^{2}}$
$[k]=\frac{[F]}{\left[v^{2}\right]}=\frac{\left[ MLT ^{-2}\right]}{\left[ L ^{2} T ^{-2}\right]}$
$=\left[ ML ^{-1} T ^{0}\right]$