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# The population in a particular area is 1000 per square kilometer.What should be the height of the transmission tower to cover a population of 10 lakhs. For the sake of simplicity, assume that the Radius of earth is 6,400 Km.

$\begin{array}{1 1}(a)\;50m\\(b)\;75m\\(c)\;25m\\(d)\;100m\end{array}$

Population density $S=1000 /Km^{2}$
$\Rightarrow 1000\times 10^{-6}m^{-2}$
$\Rightarrow 10^{-3}m^{-2}$
Let $h$ be height of tower, $d$ be radius of coverage, and $R$ the radius of earth $\rightarrow$ $d=\sqrt{2Rh}$
Population covered =$S\pi d^2 = 2\pi RSh$
$10\; \text{Lakhs} = 10 \times 10^5 = 2 \times \pi \times 6400\times 10^3 \times 10^{-3}\times h$
$\Rightarrow h=25m$
Hence (c) is the correct answer.
edited Mar 23, 2014