JEE Main · 2023 · 08 Apr 2023 · Shift 1 · EM Waves

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A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

(A) $1240 km^{2}$
(B) $3942 km^{2}$ ✓ Correct
(C) $4868 km^{2}$
(D) $1549 km^{2}$

Answer: (B)

Solution

The maximum line-of-sight distance from a transmitting antenna of height

h_{T}

to a receiving antenna at height

h_{R}

is:

d = 2 h_{T} R + 2 h_{R} R

Given

h_{T} = 98

h_{R} = 0

R = 6400

= 6400 \times 1 0^{3}

d = 2 \times 98 \times 6400 \times 1 0^{3} = 1254.4 \times 1 0^{6} \approx 35.4

km

The coverage area is

A = π d^{2} = 3.14 \times (35.4)^{2} \approx 3942

km²

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Single correct option

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