Modern Physics 7 Question 81

11. In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70m, then the minimum height of the transmitting antenna should be

(Radius of the earth =6.4×106m )

(a) 20m

(b) 32m

(c) 40m

(d) 51m

(Main 2019, 8 April II)

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Solution:

  1. Key Idea In line of sight communication, distance d between transmitting antenna and receiving antenna is given by

d=2RhT+2RhR

Here in figure, hR and hT is the height of receiving and transmitting antenna, respectively.

Given, d=50km=50×103m

hR=70m,R=6.4×106m

Then, distance between transmitting and

receiving antenna, i.e. d=2RhT+2RhR

50×103=2R(hT+hR)=2×6.4×106(hT+70)hT50×1033577.78.37=13.988.37=5.61 or hT=31.532m



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