A TV transmission tower has a height


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

  1. (1) $65 \mathrm{~km}(2)$

  2. (2) $48 \mathrm{~km}$

  3. (3) $80 \mathrm{~km}$

  4. (4) $40 \mathrm{~km}$

Correct Option: 1


(1) Maximum distance upto which signal can be broadcasted

$d_{\max }=\sqrt{2 \mathrm{Rh}_{\mathrm{T}}}+\sqrt{2 \mathrm{Rh}_{\mathrm{R}}}$

where $\mathrm{h}_{\mathrm{T}}$ and $\mathrm{h}_{\mathrm{R}}$ are heights of transmission tower and receiving antenna respectively.

Putting values $\mathrm{R}, \mathrm{h}_{\mathrm{T}}$ and $\mathrm{h}_{\mathrm{R}}$

$\mathrm{d}_{\max }=\sqrt{2 \times 6.4 \times 106}[\sqrt{140}+\sqrt{40}]$

or, $\mathrm{d}_{\max } \simeq 65 \mathrm{~km}$

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