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AIIMS 2011
Exam
AIIMS
Year
2011
Subject
Physics
Chapter
Communication System

AIIMS 2011 · Physics · Communication System

The area covered by a transmitting antenna of height 50 ~m is

The area covered by a transmitting antenna of height 50 m50 \mathrm{~m} is

Options

  1. A320πkm2320 \pi \mathrm{km}^2
  2. B1440 km21440 \mathrm{~km}^2
  3. C640πkm2640 \pi \mathrm{km}^2
  4. D120πkm2120 \pi \mathrm{km}^2

Correct answer

C. 640πkm2640 \pi \mathrm{km}^2

Step-by-step solution

Here, h=50mh=50 \mathrm{ m} Area covered =πd2=π×2hR=\pi d^2=\pi \times 2 h R \quad\left(\becaused^2=2=2 h R\right)wherewhereR=6.4 \times10^6 \mathrm{ m} (radiusofofearth) ∴ area covered =π×2hR=π×2×50×6.4×106=640π×106m2=640πkm2\begin{aligned} \therefore \quad \text{ area covered } =\pi \times2 h R=\pi \times2 \times50 \times6.4 \times10^6 \\ & =640 \pi \times10^6 \mathrm{ m}^2=640 \pi \mathrm{km}^2 \end{aligned}
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