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…

Question

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 &#961; 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

Aicharya · Accepted Answer

d ∝ ρ x S y F z ⇒ L ≡ M L - 3 x M T - 3 y T - 1 z ⇒ x + y = 0 , - 3 x = 1 , - 3 y - z = 0 ⇒ x = - 1 3 , y = 1 3 , z = - 1 ⇒ y = 1 n ⇒ n = 3 `

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses…

Solution