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Question: If pressure \(P\), velocity \(V\) and time \(T\) are taken as fundamental physical quantities, the d...

If pressure PP, velocity VV and time TT are taken as fundamental physical quantities, the dimensional formula of force is

A

PV2T2PV^{2}T^{2}

B

P−1V2T−2P^{- 1}V^{2}T^{- 2}

C

PVT2PVT^{2}

D

P−1VT2P^{- 1}VT^{2}

Answer

PV2T2PV^{2}T^{2}

Explanation

Solution

Let F∝PxVyTzF \propto P^{x}V^{y}T^{z}

by substituting the following dimensions :

[P]=[ML−1T−2][V]=[LT−1],[T]=[T]\lbrack P\rbrack = \lbrack ML^{- 1}T^{- 2}\rbrack\lbrack V\rbrack = \lbrack LT^{- 1}\rbrack,\lbrack T\rbrack = \lbrack T\rbrack

and comparing the dimension of both sides

x=1,y=2,z=2x = 1,y = 2,z = 2, so F=PV2T2F = PV^{2}T^{2}