A TV tower has a height of 20 m and radius of earth is \( 6.4\times10^{6}\,\mathrm{m} \). The range of tower is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 16 km
TV signals travel by line-of-sight (space wave) propagation, so the range of an antenna of height h is limited by the curvature of the earth. Since h is much smaller than the earth’s radius R, the distance to the horizon is
\( d = \sqrt{2Rh} \)
\( d = \sqrt{2\times6.4\times10^{6}\times20}\,\mathrm{m} = \sqrt{2.56\times10^{8}}\,\mathrm{m} \)
\( d = 1.6\times10^{4}\,\mathrm{m} = 16\,\mathrm{km} \)
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
\( \displaystyle d_T = \sqrt{2Rh_T} \)
where R is the radius of the earth (approximately 6400 km). \( d_T \) is also called the radio horizon of the transmitting antenna.”