A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS mode? Given radius of earth \( 6.4\times10^{6}\,\mathrm{m} \).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 45.5 km
In line-of-sight (LOS) communication each antenna can see up to its own horizon, a distance \( \sqrt{2Rh} \) for an antenna of height h on an earth of radius R. The maximum separation is the sum of the two horizon distances.
\( d_M = \sqrt{2Rh_T} + \sqrt{2Rh_R} \)
\( \sqrt{2Rh_T} = \sqrt{2\times6.4\times10^{6}\times32} = \sqrt{4.096\times10^{8}} \approx 20.2\times10^{3}\,\mathrm{m} \)
\( \sqrt{2Rh_R} = \sqrt{2\times6.4\times10^{6}\times50} = \sqrt{6.4\times10^{8}} \approx 25.3\times10^{3}\,\mathrm{m} \)
\( d_M \approx 20.2\,\mathrm{km} + 25.3\,\mathrm{km} \approx 45.5\,\mathrm{km} \)
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):
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