JEE Main · 2021 · 17 Mar 2021 · Shift 1 · EM Waves

For VHF signal broadcasting ______

km^{2}

of maximum service area will be covered by an antenna tower of height 30 m , if the receiving antenna is placed at ground. Let radius of the earth be 6400 km . (Round off to the Nearest Integer) (Take

π

as 3.14)

Answer: 1206

Solution

The line-of-sight range of a transmitting antenna of height

h

above an earth of radius

R

d = 2 R h

, so the area it serves is

A = π d^{2} = 2 π R h

With

R = 6400

km and

h = 30 m = 0.03

km,

A = 3.14 \times 2 \times 6400 \times 0.03 = 3.14 \times 384 = 1205.76 k m^{2}

Rounded to the nearest integer, the maximum service area is

1206 k m^{2}

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Integer answer

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