Question

T.V. transmission tower at a particular station has a height of 160m:(a) What is its coverage range? (b) How much population is covered by transmission, if the average population density around the tower is ${1200km}^{-2}$? (c) By how much the height of tower be increased to double its coverage range? Given radius of earth = 6400km.

• A. (a) 15255m(b) 87.24m(c) 480m
• B. (a) 45255m(b) 77.24m(c) 480m
• C. (a) 35255m(b) 77.24m(c) 280m
• D. (a) 25255m(b) 97.24m(c) 180m

Answer 1

The correct option is B

(a) 45255m

(b) 77.24m

(c) 480m

(a) Coverage range $d=\sqrt{2Rh}$

putting values

$d=\sqrt{2\times 6400\times 103\times 160}$

$=45.255km=45255m$

(b)

Population covered =(population density)×(area covered)

$P=\left(1200\right)\times \left(\pi d^2\right)$

putting values

$P=\left(2400\pi Rh\right)=2400\times 3.14\times 6.4\times 103\times 0.16$

$P=77.24m$

(c) Coverage range $\propto \sqrt{h}$

Therefore coverage range can be doubled by making height of the lower four times to 640m.

So, height of the lower should be increased by 480m.