Modern Physics 7 Question 25

26. A TV transmission tower has a height of $140 m$ and the height of the receiving antenna is $40 m$. What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Take, radius of earth $=6.4 \times 10^{6} m$ ).

(Main 2019, 10 Jan I)

(a) $65 km$

(b) $80 km$

(c) $40 km$

(d) $48 km$

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Solution:

  1. Maximum distance of transmission is given by

$$ d=\sqrt{2 R h _T}+\sqrt{2 R h _R} $$

where, $\quad h _T=$ height of transmitter, $=140 m$,

$$ h _R=\text { height of receiver }=40 m \text { and } $$

$$ R=\text { radius of earth }=6.4 \times 10^{6} m $$

Substituting values, we get

$$ d=\sqrt{2 \times 6.4 \times 10^{6}}(\sqrt{140}+\sqrt{40})=65 km $$



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