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

`P = (F)/(A) = (M^(1)L^(1)T^(-2))/(L^(2)) M^(1)L^(-1)T^(2)`
`C = L^(1) T^(-1)`
`Q = (E)/(At) = (ML^(2)T^(-2))/(L^(2)T) = MT^(3)`
`P^(x)Q^(y)C^(z) = (M^(1) L^(-1)T^(-2))^(x) (MT^(-3))^(y) (L^(1)T^(-1))^(x) = M^(0)L^(0)T^(0)`
`M^(x + y) L^(-x + z) T^(-2x - 3y -z) = M^(0)L^(0)T^(0)`
x + y = 0
`-x + 2 = 0 `
`-2x - 3y - z = 0`
All these conditions are statisfied by option (2)