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

(2) `P^(x) Q^(y) c^(z)` is dimensionless
`[ML^(-1) T^(-2)]^(x) [MT^(-3)]^(y) [LT^(-1)]^(z) prop M^(0) L^(0) T^(0)`
`M^(x + y) L^(-x + z) T^(-2x = 3y -z) prop M^(0) L^(0) T^(0)`
comparing powers of `M, L` and `T`
`x + y = 0 implies y = - x`
`-x + z = 0 implies z = x`
`-2x - 3y - z = 0`
`x` and `y` are equal and of opposite sign
`x` and `z` are equal and of same sign
`x = 1, y = -1, z = 1`