A transmitting and receiving antenna have height of d metres each. The maximum distance between them for satisfactory communication in Line-of-Sight mode (LOS) is 2d kilometers. If the radius of earth is 6400 km, then the yalue of d is

Options

A. 3.2 m
B. 6.4 m
C. 12.8 m
D. 16.0 m

Answer

C

Explanation

For satisfactory communication , maximum distance
`d_(max) = sqrt(2Rh_1) + sqrt(2Rh_2) " " …..(ii)`
Given , `d_(max) = 2d (km) " and " h_1 = h_2 = d (m)`
From eqs. (i) and (ii) , we get
`2d = sqrt(2Rh_1) + sqrt(2Rh_2) " " .....(iii)`
substituting values in eq. (iii) we ger
`2d xx 1000 = 2 sqrt( 2 xx 6400 xx 1000 xx d)`
` rArr (1000)^2 d^2 = 2 xx 6400 xx 1000 xx d`
` d = (2 xx 6400 xx 1000)/(1000 xx 1000) m = 12.8 m`