To find the distance `d` over which a signal can be seen clearly in foggy conditions, a railways-engineer uses dimensions and assumes that the distance depends on the mass density `rho` of the fog, intensity (power/area) `S` of the light from the signal and its frequency `f`. the engineer finds that `d` is proportional to `S^(1//n)`. the value of `n` is

Answer

C

Explanation

(3) `d prop rho^(x)S^(y)f^(z)`
`M^(0)L^(1)T^(0) = M^(x)L^(-3x)M^(y)T(-y)T^(-z)`
M^(0)L^(1)T^(0) = M^(x + y)L^(-3x)T^(-y-z)`
:. `x = (-1)/(3) and y = (1)/(3)`
:. `N = 3`