JEE Main · 2021 · 22 Jul 2021 · Shift 2 · EM Waves

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What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km ? The average population density around the tower is

200/ km^{2}

and the value of

R_{e} = 6.5 \times 1 0^{6} m

(A)Height $= 1800 m$

Population Covered $= 1413 \times 1 0^{8}$
(B)Height $= 1241 m$

Population Covered $= 7 \times 1 0^{5}$
(C)Height $= 1600 m$

Population Covered $= 2 \times 1 0^{5}$
(D)Height $= 1731 m$

Population Covered $= 1413 \times 1 0^{5}$ ✓ Correct

Answer: (D)

Solution

For line-of-sight transmission from a tower of height

h

the coverage radius is

d = 2 h R_{e}

, so

h = \frac{d ^{2}}{2 R _{e}} = \frac{( 150 \times 1 0 ^{3} ) ^{2}}{2 \times 6.5 \times 1 0 ^{6}} m = 1731 m

The service area is a circle of radius

150

km:

A = π d^{2} = π (150)^{2} = 7.07 \times 1 0^{4} k m^{2}

Multiplying by the density

200 k m^{- 2}

gives the population reached. The antenna must stand

1731

m high and it covers

1413 \times 1 0^{4}

people.

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Single correct option

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JEE Main · 2021 · 22 Jul 2021 · Shift 2 · EM Waves

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