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If pressure P is given by $P = \frac{a - l^{2}}{b t}$ where $l$ is length, $t$ is time, a and b are constant. Find dimensional formula of $\frac{b}{a}$

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$M^{- 1} L T$

$L^{2}$

$M^{- 1} L^{3} T$

$M^{- 1} L^{5} T$

answer is A.

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Detailed Solution

$P = \frac{a}{b t} - \frac{l^{2}}{t}$

$\Rightarrow P = \frac{a}{b t}$

$\Rightarrow \frac{a}{b} = P t$

$\frac{a}{b} = M L^{- 1} t^{- 2} T = M L^{- 1} T^{- 1}$

$\Rightarrow \frac{b}{a} = \frac{1}{M L^{- 1} t^{- 1}} = M^{- 1} L T$

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