If force (F), pressure (P) and speed (v) are fundamental quantities, then dimensional formula of time is :

{F^{\frac{1}{2}}}^{\frac{1}{2}} P^{\frac{1}{3}} v^{- 2}

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{F^{\frac{1}{2}}}^{\frac{1}{2}} P^{\frac{1}{2}} v^{- 1}

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{F^{\frac{1}{2}}}^{\frac{1}{2}} P^{\frac{- 1}{2}} v^{- 1}

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{F^{\frac{1}{2}}}^{\frac{1}{2}} P^{\frac{- 1}{2}} v^{2}

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Solution

The correct option is C ${F^{\frac{1}{2}}}^{\frac{1}{2}} P^{\frac{- 1}{2}} v^{- 1}$
$P = \frac{F}{A}$
$A = \frac{F}{p}$
$v = \frac{L}{t i m e}$ $t i m e = \frac{L}{v} = \frac{\sqrt{A}}{v} = \frac{\sqrt{(F / P)}}{v} = F^{\frac{1}{2}} P^{\frac{- 1}{2}} v^{- 1}$

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