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What should be the height of transmittin...

What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km ? The average population density around the tower is `2000//km^2` and the value of `R_e = 6.5 xx 10^(6)` m.

A

Height = 1800 m
Population Covered = `1413xx10^8`

B

Height = 1600m
Population covered `= 2xx10^5`

C

Height = 1731 m
Population covered = `1413xx10^5`

D

Height = 1241m
Population covered `= 7xx10^5`

Text Solution

Verified by Experts

The correct Answer is:
C
Radius of earth `R_e = 6.5xx10^6` m
`d=150 km`
Height of Antenna = ?
`d=sqrt(2Rh)`
`h = d^2/(2R)=(150xx150 xx10^6)/(2xx6.5 xx10^6)=1730 .7~~1731m`
Population covered `implies 2 piRhxx` density
`2pixx6.5xx10^6 xx1730.7xx2000xx10^(-6) ~~ 1413xx10^5`
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