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^(0)L^(1)T^(-1), (T)= M^(0)L^(0)T^(-1)`
`:. MLT^(-2)= (ML^(-1)T^(-2))^(a)(M^(0)L^(0)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)`.