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A TV tower has a height of 100m. How much population is covered by the TV broadcast if the average population density around the tower is 1000 per sq.km. Radius of the earth $6.37 \times 10^{6} m .$ By how much height of the tower be increased to double its coverage range (in m)?

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answer is 300.

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Detailed Solution

$h' = 2 d = 2 \sqrt{2 h R} \Rightarrow h' = 4 h = 400 m$
Increase in height $= h' - h = 300 m$

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