Discussion Forum

To find the distance d over which a signal can be seen clearly in foggy conditions, a  railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ 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:

Explanation:

Let    $d=k(\rho)^{a}(S)^{b}(f)^{c}$

 where, k is a dimensionless, then

$[L]=\left[ \frac{M}{L^{3}}\right]^{a}\left[\frac{ML^{2}T^{-2}}{L^{2}T}\right]^{b}\left[\frac{1}{T}\right]^{c}$

 Equating  the powers of M and L , we have

       0=a+b      ........(i)

           1= -3a...........(ii)

Solving these two equations , we get

    $b=\frac{1}{3}$                $\therefore n=3$