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

If pressure P, velocity V and Time T are taken as fundamental physical

1.	If pressure P, velocity V and Time T are taken as fundamental physical quantities the dimensional formula of the force is
Answer» SOLUTION :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)`