question_answer

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 \[=6.4\times {{10}^{6}}m\]) is :   AIEEE  Solved  Paper-2012

A)  80 km                     

B) 16 km

C) 40 km                      

D) 64 km

Correct Answer: A

Solution :

             \[r=R+h\cong R\] \[x=\sqrt{{{(R+h)}^{2}}-{{R}^{2}}}\]              \[=\sqrt{{{h}^{2}}+2hR}\] \[{{x}^{2}}=25000+2.500\,\,\,6.4\,\,100000\]    \[=25000+\,\,(64\times \,\,100000000)\]    \[={{10}^{4}}(640025)\] \[{{x}^{2}}\cong {{10}^{4}}.640000\] \[x=8\times {{10}^{4}}m\] \[=80\] km.