If pressure P, velocity V and time T are taken as fundamental physical quantities, then the dimensional formula for force is

P V^{2} T^{2}

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P^{- 1} V^{2} T^{- 2}

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P V T^{2}

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P^{- 1} V T^{2}

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Solution

The correct option is A $P V^{2} T^{2}$
$K \propto P^{x} V^{y} T^{z}$ writing the dimensional formulae on both sides $M L T^{- 2} = [M L^{- 1} T^{- 2}]^{x} . [L T^{- 1}]^{y} . T^{z}$ , equating the powers of M, L and T on both sides we get x = 1, y = 2 and z = 2.
$∴ F = P V^{2} T^{2}$

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If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force is

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