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

Explanation

Let force = `F = P^a V^b T^c`
`(F) = M^1 L^1 T^(-2), (P) = M^1 L^(-1)T^(-2)`
`(V) = M^0 L^1 T^(-1), (T) = M^0 L^0 T^1`
`:. MLT^(-2) = (ML^(-1) T^(-2))^a (M^0 L^1 T^(-1))^b (M^0 L^0 T^1)^c`
`MLT^(-2) = M^a L^(-a + b) T^(-2a - b + c)`
`:.` Comparing powers of `M, L , T` on both sides
`a = 1, - a + b = 1 :. b = 2 and -2a - b + c = -2 , -2 -2 + c = -2 , c = 2`
`:.` Force `(F) = PV^2 T^2`.