JEE Main · 2021 · 16 Mar 2021 · Shift 2 · EM Waves

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Two identical antennas on identical towers are separated from each other by a distance of 45 km . What should be the minimum height of receiving antenna to receive the signals in line of sight? (Assume radius of earth is 6400 km )

(A)79.1 m
(B)19.77 m
(C)39.55 m✓ Correct
(D)158.2 m

Answer: (C)

Solution

An antenna of height

h

on a spherical earth of radius

R

sees the horizon at a distance

2 R h

. The two towers are identical, so each covers that much of the gap and the line-of-sight separation is

d = 2 R h + 2 R h = 2 2 R h \Rightarrow h = \frac{d ^{2}}{8 R}

With

d = 45 km = 4.5 \times 1 0^{4} m

and

R = 6400 km = 6.4 \times 1 0^{6} m

h = \frac{( 4.5 \times 1 0 ^{4} ) ^{2}}{8 \times 6.4 \times 1 0 ^{6}} = \frac{2.025 \times 1 0 ^{9}}{5.12 \times 1 0 ^{7}} = 39.55 m

The receiving antenna must stand at least

39.55 m

high.

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Single correct option

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JEE Main · 2021 · 16 Mar 2021 · Shift 2 · EM Waves

Solution

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