# What should be the height of transmitting antenna and

Question:

What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of $150 \mathrm{~km}$ ? The average population density around the tower is $2000 / \mathrm{km}^{2}$ and the value of $\mathrm{R}_{\mathrm{e}}=6.5 \times 10^{6} \mathrm{~m}$.

1. Height $=1731 \mathrm{~m}$

Population Covered $=1413 \times 10^{5}$

2. Height $=1241 \mathrm{~m}$

Population Covered $=7 \times 10^{5}$

3. Height $=1600 \mathrm{~m}$

Population Covered $=2 \times 10^{5}$

4. Height $=1800 \mathrm{~m}$

Population Covered $=1413 \times 10^{8}$

Correct Option: 1

Solution:

Radius covered $r=\sqrt{2 \mathrm{RH}_{\mathrm{T}}}$

$150 \mathrm{~km}=\sqrt{2 \times\left(6.5 \times 10^{6} \mathrm{~m}\right) \mathrm{H}_{\mathrm{T}}}$

$\left(150 \mathrm{~km} \times 10^{3}\right)^{2}=2 \times 6.5 \times 10^{6} \mathrm{H}_{\mathrm{T}}$

$\mathrm{H}_{\mathrm{T}}=1731 \mathrm{~m}$

Population covered $=\left(\pi r^{2}\right)\left(2000 / \mathrm{km}^{2}\right)$

$=3.14 \times(150)^{2} \times 2000=1413 \times 10^{5}$