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

Explanation

Let d is the maximum distance, upto which it can detect the objects
From `DeltaAOC`
`OC^(2)=AC^(2)+AO^(2)`
`(h+R)^(2)=d^(2)+R^(2)`
`impliesd^(2)=(h+R)^(2)-R^(2)`
`impliesd^(2)=(h+R)^(2)-R^(2)`
`d=sqrt((h+R)^(2)-R^(2))`
`d=sqrt(h^(2)+2hR)`
`d=sqrt(500^(2)+2xx6.4xx10^(6))=80km`