Q 12-14-148JEE MainJEE Main 2021 (22 Jul, Shift 1)Medium
What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km? The average population density around the tower is $2000\ \text{km}^{-2}$ and the value of $R_e = 6.5\times10^6$ m.
Answer: (A) Height = 1731 m, Population Covered = $1413\times10^5$
$d = \sqrt{2Rh} \Rightarrow h = \dfrac{d^2}{2R} = \dfrac{(1.5\times10^5)^2}{2\times6.5\times10^6} \approx 1731$ m.
Area covered $= \pi d^2 = 3.14\times150^2 \approx 7.07\times10^4\ \text{km}^2$. Population $= 7.07\times10^4\times2000 \approx 1.413\times10^8 = 1413\times10^5$.
Solution by Sreeraj P, M.Sc Physics