JEE Main · 2023 · 11 Apr 2023 · Shift 1 · EM Waves

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A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is

x \times 1 0^{- 2} m

. The value of x is (Let. radius of earth

R = 6400 km

)

(A)125✓ Correct
(B)12.5
(C)1.25
(D)1250

Answer: (A)

Solution

For line-of-sight reception from an antenna on the ground, the range to a receiver of height

h_{r}

d = 2 h_{r} R

. Solving,

h_{r} = \frac{d ^{2}}{2 R} = \frac{( 4 ) ^{2}}{2 ( 6400 )}

= \frac{16}{12800}

= 1.25 \times 1 0^{- 3}

= 1.25

m. Written as

x \times 1 0^{- 2}

m this is

125 \times 1 0^{- 2}

m, so

x = 125

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option

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