Question

A TV transmission tower antenna is at a height of 20 m. The percentage increase in area covered in case if the receiving antenna is at ground level to that at a height of 25 m is

(Radius of earth = 6.4 x 106 m)

• A. 248%
• B. 348.9%
• C. 150%
• D. 360.2%

Answer 1

Answer: (B)

348.9%

Answer 2

: Here , $h_{T} = 20m,R = 6.4 \times 10^{6}m = 64 \times 10^{5}m$

If the receiving antenna is at ground level

Range, $d = \sqrt{2h_{T}R} = \sqrt{2 \times 20 \times (64 \times 10^{5})}$

$= 16 \times 10^{3}m = 16km$

Area covered

$A = \pi d^{2} = \frac{22}{7} \times (16)^{2} = 804.6km^{2}$

If the receiving antenna at a height of 25 m

Range $d_{1} = \sqrt{2h_{T}R} + \sqrt{2h_{R}R}$

$= \sqrt{2 \times 20 \times (64 \times 10^{5})} + \sqrt{2 \times 25 \times 64 \times 10^{5}}$

}{= 33.9 \times 10^{3}m = 33.9km}$$