Question

A TV transmission tower at a particular station has a height of 160m. Radius of earth is 6400km
i. The range it covers is 45255m
ii. The population that it covers is77.42 lakhs.
iii. The height of antenna should be increased by 480m to double the coverage range

• A. i and ii are true
• B. ii and iii are true
• C. i and iii are true
• D. i, ii and iii are true

Answer 1

The correct option is D i, ii and iii are true

Given : Height of tower $h_T=160$ m

Radius of earth $R=6400km=6.4\times {10}^6$ m

Population density $\rho =1200$ $k{m}^{-2}$

(i) : Range it covers $d_T=\sqrt{2R{h}_T}=\sqrt{2\times 6.4\times {10}^6\times 160}$ $=45255$ m

(ii) : Area covered $A=\pi d_T^2=3.14\times (45255{)}^2$ $m^2=6.431\times {10}^9$ $m^2=6431$ $k{m}^2$

Population covered $P=\pi d_T^2\times \rho =6431\times 1200=77.42$ lakhs

(iii) : $d_T\propto \sqrt{h_T}$ $⟹\frac{h_T^{\prime }}{h_T}=\frac{d_T^{\prime 2}}{d_T^2}$

$\therefore \frac{h_T^{\prime }}{160}=2^2$ $⟹h_T^{\prime }=640$ m

Thus increase in height of tower $\Delta h_T=640-160=480$ m