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