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

Options

A. `x=1,y=1,z=1`
B. `x=1,y=1,z=-1`
C. `x=-1,y=1,z=1`
D. `x=1,y=-1,z=1`

Answer

D

Explanation

`P=("Force")/("area")=(MLT^(-2))/(L^(2))=ML^(-1)T^(-2)`
`c=[LT^(-1)]`
and `Q=("Energy")/("area" xx "time")=(ML^(2)T^(-2))/(L^(2)T)=[ML^(0)T^(-3)]`
Now `P^(x)Q^(y)C^(z)=[M^(x)L^(-x)T^(-2x)][M^(y)T^(-3y)][L^(z)T^(-z)]`
`P^(x)Q^(y)C^(z)=M^(x+y)L^(-x+z)T^(-2x-3y-z)`
`P^(x)Q^(y)C^(z)` to be dimensionless.
`x+y=0,-x+z=0,-2x-3y-z=0`
Also it is given that `x,y,z` are to be non-zero `i.e` least value of `x` should be. `1`. Thus if `x=1,` then `y=-1` and `z=1` will satisfy the above equations. Therefore, we get `x=`,`y=-1` and `z=1`.
Hence correct choice is `(d)`.