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1.Units, Dimensions and Measurement
normal
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 find that $d$ is proportional to $S ^{1 / n}$. The value of $n$ is:
A
$3$
B
$4$
C
$5$
D
$6$
(IIT-2014)
Solution
$d=k \quad(\rho)^a \quad(S)^b \quad(f)^c $
${\left[\frac{M}{L^3}\right]^a\left[\frac{M^1 L^2 T^{-2}}{L^2 T}\right]^b\left[\frac{1}{T}\right]^c} $
$0=a+b $
$1=-3 a \quad \Rightarrow a=-\frac{1}{3} \quad \text { So : } b=\frac{1}{3} $
$0=-3 b+c$
So : $n=3$
Standard 11
Physics
