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

Options

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

Answer

A

Explanation

(a) Let height of `TV` antenna be `h` and radius of earth is `R` and `R gt gt h`.
Let `M` be receiving station when `h lt lt R` the `NM` may be assumed as tangent to the surface of earth, so
`/_ NMC = 90^(@)`
`implies NC^(2) = NM^(2) + MC^(2)`
`implies (R + h)^(2) = NM^(2) + R^(2)`
`implies NM^(2) = R^(2) + h^(2) 2 Rh - R^(2)`
`= 2Rh + h^(2)`
Since, `h lt lt R`
So, `h^(2)` may be neglected hence, `NM^(2) = 2 R`
`implies NM prop h^((1)/(2))`