A TV tower has a height of 200 m. The population covered by TV broadcast would be (radius of earth = \( 6.4\times10^{6}\,\mathrm{m} \) and the average density of population = \( 10^{3}\,\mathrm{km^{-2}} \))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 80 lakh
A TV tower of height h covers a circular region whose radius is the line-of-sight distance \( d = \sqrt{2hR} \), where R is the radius of the earth. The population covered is the area of this circle multiplied by the population density.
\( \text{Area} = \pi d^{2} = 2\pi hR = 2\times3.14\times200\times6.4\times10^{6}\,\mathrm{m^{2}} \)
\( \text{Area} \approx 8.04\times10^{9}\,\mathrm{m^{2}} = 8.04\times10^{3}\,\mathrm{km^{2}} \)
\( \text{Population} = 8.04\times10^{3}\times10^{3} \approx 8.0\times10^{6} \)
Since 1 lakh = \( 10^{5} \), this is about 80 lakh.