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

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$[P^{1} V^{1} T^{1}]$

$[P^{1} V^{2} T^{1}]$

$[P^{1} V^{1} T^{2}]$

$[P^{1} V^{2} T^{2}]$

answer is D.

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Detailed Solution

$P = M L^{- 1} T^{- 2} \Rightarrow M = P L T^{2} = P V T T^{2} = P V T^{3} V = L T^{- 1} \Rightarrow L = V T N o w f o r c e = M L T^{- 2} = P V T^{3} \times V T \times T^{- 2} = p V^{2} T^{2}$

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