Question

A radar has a power of $1kW$ and is operating at a frequency of $10GHz$. It is located on a mountaintop of height $500m$. The maximum distance up to which it can detect object located on the surface of the earth (Radius of earth $=6.4\times {10}^{6}m)$ is

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

Answer 1

Answer: (A)

$80km$

Let Maximum distance on earth where object can be detected is d, height of mountain is h, R=Radius of earth

$R=6.4\times {10}^{6}m$

$h=500m$

$(h+R{)}^2=d^2+R^2$

since $h<<R,d^2=2hR$

$d=\sqrt{2hR}$

$d=\sqrt{64\times {10}^8}$

$d=8\times {10}^{4}m$

Hence the correct option is (D)