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Question:

A radar has a power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mountain top, of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth is:(Radius of earth=6.4×106m)

64 km

16 km

80 km

40 km

Solution:

Maximum distance on earth where object can be detected is d, then
(h+R)2=d2+R2
d2=h2+2Rh
Since h<<R, d2=2Rh
d=√2(500)(6.4×106)=80km