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^(-1)T^(-2)]^(0) [MT^(-2)] [LT^(-1)]^(0) = [MLT]^(0)`
By comparing the power to M,L,T in sides
`x + y = 0`…(i)
`- x + z = 0`…(ii)
`-2x - 3y - z = 0`…(iii)
The only value of x, y, z, satisfiying (i),(iii) corresponds to (b)