If pressure P, velocity V and Time T are taken as fundamental physical quantities the dimensional formula 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, -1 + b=1 therefore b=2 and -2a -b+ c = -2, -2 -2 -2 + c = -2 , c=2`
`therefore` Force (F) `= PV^(2) T^(2)`