A TV tower has a height of 200 m. the population covered by TV broadcast would be (radius of earth = $6.4 \times 10^6 m$ and the average density of population = $10^3 Km^{-2}$)

80 lakh

The correct answer is Option (3) → 80 lakh

The distance of horizon, d for a point above the earth's surface can be found using the formula:

$d=\sqrt{2hR}$

where,

$h = 200 m$ [given]

$R = 6.4×10^6m$ [given]

$d=\sqrt{2×200×6.4×10^6}$

$=5.06×10^4m=50.6km$

∴ A, Area covered by TV signal = $\pi d^2$

$=\pi (50.6)^2$

$=8042.8km^2$

Population covered = $8042.8×10^3$

= 80,42,000 people

≃ 80 lakh