If pressure P, velocity V and time T are taken as fundamental physical quantities , the dimensional formulae of the 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)`
`therefore 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)`
`therefore` Comparing powers of M, L, T on both sides
`a=1, -a+b=1 therefore b=2 and -2a- b+c = -2, -2 -2 =c = -2, c=2`
`therefore` Force (F) `= PV^(2)T^(2)`