If pressure P, velocity v and time T are taken as the fundamental (base) quantities, find the dimensional formula of force.

If pressure P, velocity v and time T are taken as the fundamental (bas

1.	If pressure P, velocity v and time T are taken as the fundamental (base) quantities, find the dimensional formula of force.
Answer» <P> 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, -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)`