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.

Question

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.

Infinity Learn · Accepted Answer

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 × π$$d2$$ $$=1200$$×$$3.14$$×(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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