The dimensional formula of the product of two physical quantities P and Q is `ML^2 T^(-2)`. The dimensional formula of `P//Q` is `ML^0 T^(-2)`. Then what are the units of physical quantities P and Q.

Explanation

Given `P xx Q` has dimensions `ML^(2)T^(-2)`
P/Q has dimensions `ML^(0) T^(-2)`
Henc, `(PQ) ((P)/(Q)) = (ML^(2)T^(2)) (ML^(0)T^(-2))`
`P^(2)= M^(2)L^(2)T^(-4)`
`therefore P= ML^(1) T^(-2)`= Force ….(1) given `(P)/(Q)= M^(1) L^(0) T^(-2), (ML^(1) T^(-2))/(Q)= ML^(0)T^(-2)`
`Q= (ML^(1) T^(-2))/(ML^(0)T^(-2))= L`= Displacement.....(2)
`therefore P and Q` are respectively the force and the displacement, hence their units are newton and metre.