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

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^) 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^0T^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`