A radar has a power of `1kW` and is operating at a frequency of `10 GHz`. It is located on a mountain top of height `500m`. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth `6.4xx10^(6)m`) is

Options

A. 80 km
B. 16 km
C. 40 km
D. 64 km

Explanation

Here, h=500m, R=6.4xx10^(6)m`
Let O be the mountain top where a radar has been operating to locate the objects on earth, Fig. 10(CF).4.
Let d(OA=OB) be the maximum distance of radar from earth where object can be detected.
Refer to Fig. 10(CF).4.
`d^(2)+R^(2)=(h+R)^(2)=h^(2)+2hR+R^(2)`
or `d^(2)=h^(2)+2hR`

Since `hltltR`, so `h^(2)` can be neglected in comparison to 2hR.
or `d=sqrt(2hR_=sqrt(2xx500xx(64)xx10^(6))`
`=80xx10^(3) m=80km`