$A$ radar has a power of $1 \text{ kW}$ and operates at a frequency of $10 \text{ GHz}$. If it is located on top of a mountain at a height of $500 \text{ m}$,what is the maximum distance in $\text{km}$ up to which it can detect objects on the Earth's surface? (Radius of the Earth $R = 6.4 \times 10^{6} \text{ m}$)

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

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