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`.

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

B

Explanation

By substituting the dimension of given quantities `[ML^-1T^-2]^x[MT^-2]^y[LT^-1]^z=[MLT]^0`
comparing the power of M, L, T in both sides
`x+y=0` ..(i)
`-x+z=0` .(ii)
`-2x-2y-z=0` .(iii)
The only values of x,y,z satisfying (i),(ii) and (iii) corresponds to (b).