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

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 ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer find that d is proportional to S 1/ n . The value of n is:

TestHub · Accepted Answer

d ∝ ρ a S b f c [ ρ ] = M L − 3 , [ S ] = M T − 3 , [ f ] = T − 1 Equating powers of mass and length: a + b = 0 , − 3 a = 1 a = − 3 1 ​ , b = 3 1 ​ The time power also gives: − 3 b − c = 0 ⇒ c = − 1 d ∝ S 1/3 ⇒ n = 3

Physics - Unit & Dimension Question with Solution | TestHub

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