General Physics Question 22

Question 22

  1. To find the distance d over which a signal can be seen clearly in foggy conditions, a railway 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 S1/n. The value of n is

(2014 Adv.)

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Answer:

Correct Answer: 30. (d)

Solution:

  1. Let d=k(ρ)a(S)b(f)c

where, k is a dimensionless. Then,

[L]=Ma L3ML2 T2 L2 T1 T

Equating the powers of M and L, we have

0=a+b 1=3a

Solving these two equations, we get

b=13⇒∴n=3



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