If pressure ' $p$ ' depends upon velocity ' $v$ ' and density ' $d$ ', the relationship between $p, v$ and $d$ is:

p \propto v d

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p \propto v^{2} d

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p \propto \frac{v^{3}}{d}

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p \propto \frac{v^{2}}{d^{2}}

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Solution

The correct option is D $p \propto v^{2} d$
$P = v^{α} d^{β}$
$M^{1} L^{- 1} T^{- 2} = (L T^{- 1})^{α} (M L^{- 3})^{β}$
$M^{1} L^{- 1} T^{- 2} = M^{β} L^{- 3 β + α} T^{- α}$
$\Rightarrow β = 1$
$- 3 β + α = - 1$ $\Rightarrow α = 2$
$- α = - 2$ $\Rightarrow α = 2$
So, $p \propto v^{2} d$

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