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

Correct answer: A. 80 ~km Maximum distance on earth where object can be detected is d , then array ll & (h+R)^2=d^2+R^2 & d^2=h^2+2 R h since & h

JEE Main 2012Offline

JEE Main 2012 · Offline · Physics · Communication System

A radar has a power of 1 ~Kw and is operating at a frequency of 10...

A radar has a power of

1 \mathrm{~Kw}

and is operating at a frequency of

10 \mathrm{~GHz}

. It is located on a mountain top of height

500 \mathrm{~m}

. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth

=6.4 \times 10^6 \mathrm{~m}

) is

A. $80 \mathrm{~km}$

Maximum distance on earth where object can be detected is

\mathrm{d}

, then

\begin{array}{ll} & (h+R)^2=d^2+R^2 \\ \Rightarrow & d^2=h^2+2 R h \\ \text{ since } & h < < R, \quad \Rightarrow d^2=2 h R \\ \Rightarrow & d=\sqrt{2(500)\left(6.4 \times 10^6\right)}=80 \mathrm{~km} \end{array}