A TV tower has a height of $5 \mathrm{~m}$ in a region of population density $\frac{1000}{\pi}$ per square…
A TV tower has a height of $5 \mathrm{~m}$ in a region of population density $\frac{1000}{\pi}$ per square kilometre. Number of people that can receive the transmission is nearly, (in thousands)
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Solution
Given, height of a TV tower, $h=5 \mathrm{~m}$ population density, $n=\frac{1000}{\pi}$
Now, the maximum range of this transmission depends upon the height of transmitting antenna and is given by $d=\sqrt{2 h R_e}$.
where, $h=$ height of tower
and $R_e=$ Radius of earth $(R>>h)$
So, the number of people received the transmission,
Population covered, $\left(P_c\right)=$ population density $(n) \times$ area of transmission range $(\mathrm{A})$
Population covered, $\left(P_c\right)=n \times A$
$
P_c=\frac{1000}{\pi} \times \pi d^2
$
Area of transmission range,
or
$
\begin{gathered}
A=\pi d^2 \text { or } P_c=1000 \times 2 h R_e \quad\left[\because d^2=2 h R_e\right] \\
P_c=1000 \times 2 \times 5 \times 10^{-3} \times 6400 \\
P_c=64000
\end{gathered}
$
So, the number of people received the transmission is 64000