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Q.

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 ρof the fog, intensity (power/ area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S1n. The value of n is

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a

3

b

5

c

6

d

1

answer is A.

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Detailed Solution

Let d = kρaSbfcwhere, k is dimensionless. Then,[L] = [ML3]a[ML2T-2L2T]b[1T]c[L] = [Ma+bL-3aT-3b-c]Equating the powers of M and L, we get0 = a+b   …(i)1 = -3a     … (ii)Solving these two equations, we getb = 13 = 1n  ⇒ n = 3
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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 ρof the fog, intensity (power/ area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S1n. The value of n is