The dimensional formula of a/b in the equation $P = \frac{a - c t^{2}}{b x}$ where P = pressure, x = displacement and t = time

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$[M T^{2}]$

$[L T^{2}]$

$[M T^{- 2}]$

$[L T^{- 2}]$

answer is A.

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Detailed Solution

Apply principle of Homogeneity

$\begin{aligned} [pressure] = [\frac{force}{area}] = [\frac{a}{bx}] \\ or [{ML}^{- 1} T^{- 2}] = [\frac{a}{b}] [\frac{1}{L}] \\ or [\frac{a}{b}] = [{MT}^{- 2}] \end{aligned}$

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