The maximum distance upto which ` TV` transmission from a ` TV` tower of height `h` can be received is proportional to

Options

A. `h`
B. `h^(3//2)`
C. `h^(1//2)`
D. `h^(2)`

Answer

C

Explanation

Let height of `TV` antenna be `h` and radius of earth is `R` and `Rgt gth`.

Let `M` be the receive station when `h lt lt R` then `NM` may be assumed as tangent to the surface of earth, so
`angleNMC=90^(@)`
`:. NC^(2)=NM^(2)+MC^(2)`
`(R+h)^(2)=NM^(2)+R^(2)`
`implies NM^(2)=R^(2)+h^(2)+2Rh+h^(2)`
Since, `hlt ltR`
So, `h^(2)` may be neglected, hence `NM^(2)=2Rh`
`implies NM proph^(1/2)`