InterviewSolution
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InterviewSolution
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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 |
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Answer» Correct Answer - `3` `d = rho^(a) S^(b) f^( c)` ` d = ((kg)/( m^(3)))^(a) xx (( w)/(m^(2))) ^(b) xx ((1)/( sec))^(c )` `d = (ML^(-3))^(a) ((ML^(2) T^(-3))/(L^(2)))^(b) ((1)/( sec))^( c )` `L^(1) = M^(a + b L^(-3a) T^(-3b -c )` ` -3a = 1 rArr a = -(1)/(3)` ` a + b = 0` `( :. b = (1)/(3))` `- 3b -c = 0` `( :. c = 1)` `:. rho^-(1)/(3) S^(1)/(3) f^(1)` `:. d prop S^(1//n) ( :. n = 3)` |
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