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 dimensional analysis 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. 4B. 2C. 3D. 1 |
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Answer» Correct Answer - C Let `dproprho^(x)S^(y)f^(z)` or `d=krho^(x)S^(y)f^(z)` where k is a dimensionless constant and x,y and z are the exponents. Writings dimenions on both sides, we get `[M^(0)LT^(0)]=[ML^(-3)T^(0)]^(x)[ML^(0)T^(-3)]^(y)[M^(0)L^(0)T^(-1)]^(z)` `[M^(0)LT^(0)]=M^(x+y)L^(-3x)T^(-3y-z)]` applying the principle of homogeneity of dimensions, we get ltBrgt `x+y=0` . . . (i) `-3x=1` . . . .(ii) `-3-z=0` . . . (iii) Solving eqns. (i), (ii) and (iii), we get `x=-(1)/(3),y=(1)/(3),z=-1,` as `dpropS^(1//3)` `thereforen=3` |
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