A TV tower has a height of 160 m. How much population is covered by the television broadcast, if the average population density around the tower is 1000 per km2? Given radius of the earth is 6400 km.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 64.3 lacs
A TV signal travels in a straight line (line-of-sight propagation), so the tower covers a circle whose radius is the distance to the horizon, \( d = \sqrt{2Rh} \), where R is the radius of the earth and h the height of the tower. The population covered is the area of this circle times the population density.
\( R = 6400\,\mathrm{km} = 6.4\times10^{6}\,\mathrm{m},\quad h = 160\,\mathrm{m} \)
\( d^{2} = 2Rh = 2\times6.4\times10^{6}\times160 = 2.048\times10^{9}\,\mathrm{m^{2}} \)
Area covered:
\( A = \pi d^{2} = 3.14\times2.048\times10^{9}\,\mathrm{m^{2}} \approx 6.43\times10^{9}\,\mathrm{m^{2}} = 6.43\times10^{3}\,\mathrm{km^{2}} \)
\( \text{Population} = 1000\,\mathrm{km^{-2}}\times6.43\times10^{3}\,\mathrm{km^{2}} = 6.43\times10^{6} \)
\( 6.43\times10^{6} = 64.3\times10^{5} = 64.3 \) lacs
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Space Wave – “… If the transmitting antenna is at a height \( h_T \), then you can show that the distance to the horizon \( d_T \) is given as \( d_T = \sqrt{2Rh_T} \), where R is the radius of the earth (approximately 6400 km). \( d_T \) is also called the radio horizon of the transmitting antenna.”