If `P` represents radiation pressure , `C` represents the speed of light , and `Q` represents radiation energy striking a unit area per second , then non - zero integers `x, y, z` such that `P^(x) Q^(y) C^(z)` is dimensionless , find the values of `x, y , and z`.

Explanation

`Here, p = (MLT^(-2))/(L^2) = [ML^(-1) T^(-2)]`
`c= [LT^(-1)]`
`q = ("energy")/("area"xx"time") = (MLT^(-2))/(L^2 T) = [MT^(-3)]`
`:. P^x q^y x^z = (ML^(-1) T^(-2))^(x) (MT^(-3))^(y)(LT^(-1))^z = M^(x+y) L^(-x+z) T^(-2x - 3y -z)`
It will be dimensionless, If x+ y =0 :. x = -y
-x+z= 0and x =z
-2x - 3y -z =0
These equations have infinite solutions. One of the solutins is x = 1, y -1 and z =1, so that `p^x q^y c^z` is dimensionless.