JEE Advanced 2014 · Paper 1 · Physics Q15

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PhysicsInteger+3Question 15 of 60

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

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Answer and worked solution

Official answer: 3

Dimensions. Write $d=k\rho^aS^bf^c$ with $[\rho]=\mathrm{ML^{-3}}$ , $[S]=\mathrm{MT^{-3}}$ (power per area) and $[f]=\mathrm T^{-1}$ .

$\mathrm L^1=\mathrm M^{a+b}\,\mathrm L^{-3a}\,\mathrm T^{-3b-c}.$

L: $-3a=1$ , so $a=-\frac13$ .
M: $a+b=0$ , so $b=\frac13$ .
T: $c=-3b=-1$ .

So $d\propto S^{1/3}$ and $n=3$ .

Answer: 3

Topics:Dimensional analysis

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JEE Advanced 2014 · Paper 1, Physics question 15