A TV transmission tower antenna is at a height of 20m. The percentage increase in area covered in case if the receiving antenna is at ground level to that at a height of 25 m is (Radius of earth `=6.4xx10^(6)m`)

Options

A. 2.48
B. `348.9%`
C. `150%`
D. `360.2%`

Answer

B

Explanation

Here, `h_(T)=20m,R=6.4xx10^(6)m=64xx10^(5)m`
If the anteena is at ground level
Range, `d=sqrt(2h_(T)R)=sqrt(2xx20xx(64xx10^(5)))`
`=16xx10^(3)m=16km `
Area covered, `A=pid^(2)=(22)/(7)xx(!6)^(2)=804.6km^(2)`
If the receiving antenna at a height of 25m.
Range `d_(1)=sqrt(2h_(T)R)_sqrt(2h_(R)R)`
`=sqrt(2xx20xx(64xx10^(5)))+sqrt(2xx25xx64xx10^(5))`
`=16xx10^(3)+17.9xx10^(3)=33.9xx10^(3)m=33. 9km`
Area covered `A_(1)=pid_(1)^(2)=(22)/(7)xx(33.9)^(2)=3611.8km^(2)`.
percentage increase in area `=(A_(1)-A)/(A)xx100`
`=((3611.8-804.6)/(804.6))xx100=348. 9%`