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

Options

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

Answer

A

Explanation

If the height of the antenna is h, then the maximum distance upto which the TV transmission for a TV tower can be received is proportional to `h^(1//2)`.
Suppose that the height of the TV antena be h and the radius of the earth be R and R gtgt h. Let A be a receiving station. In the limit h ltlt R, we can assume that BA is a tangent to the surface of the earth. Then `angle BAO = 90^@` and so
`BO^2 = AB^2 + AO^2 rArr (R+h)^2 = AB^2 + R^2`
`rArr AB^2 = R^2 + h^2 + 2Rh - R^2=2Rh + h^2`
as h ltlt R we neglect `h^2` and so
`AB^2 = 2Rh rArr AB= sqrt(2Rh)`
`therefore AB prop h^(1//2)`.