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Q.

A TV transmission tower at a particular station has a height of 160 m radius of earth is 6400 km.i.  The range it covers is 45255 m (approx).ii.  The population that it covers is  77.2 lakhs (approx) when population density is  1200km−2iii. The height of antenna should be increased by 480 m to double the coverage range.

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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 is D.

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Detailed Solution

Given :  h=160 m = 160×10−3km = 0.16 km R=6400 km , P.D = 1200km−2   i)  d = 2Rh=2×0.16×6400 = 322km=45.255km  ii)  Population =P.d × πd2 =1200×3.14×(322)2 = 77,20,778  iii)  d = 2Rh   ⇒d∝h ∴d2d1=h2h1 ⇒2dd=h2160 ⇒h2=4×160=640 ⇒Increase in height = h2−h1=640−160=480 m
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