Question

To find the distance `d` over which a signal can be seen clearly in foggy conditions, a railways-engineer uses dimensions and assumes that the distance depends on the mass density `rho` 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
A. `3`
B. `5`
C. `6`
D. `1`

Answer 1

Correct Answer - a
Let `d = k rho^(a) S^(b)f^(c)`
where k is dimensionless Thus
`[L] = [(M)/(L^(3))]^(a) [(ML^(2)T^(-2))/(L^(2)T)]^(b) [(1)/(T)]^(c)`
`[L] = [M^(a+b) L^(-3a)T^(-3b - c)]`
Equating the powers of M and L we get
`0 = a+b…(i)`
`1 = -3a...(ii)`
Solving these two equation we get
`b = (1)/(3) = (1)/(n) rArr n = 3`