A radar has a power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mount

Name: Problem 73, Chapter 28: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-15T10:48:21-08:00
Duration: 1 min 1 s
Channel: Hast Aggarwal
Description: 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 (Radius of earth =6.4 ×10^6 m ) is [AIEEE 2012] (a) 80 km (b) 16 km (c) 40 km (d) 64 km

step 1 So let's solve this question. So the question asks us, a radar has a power of 1 kilowatt and ope

Question

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 [AIEEE 2012] (a) $80 \mathrm{~km}$ (b) $16 \mathrm{~km}$ (c) $40 \mathrm{~km}$ (d) $64 \mathrm{~km}$

   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 [AIEEE 2012]
(a) $80 \mathrm{~km}$
(b) $16 \mathrm{~km}$
(c) $40 \mathrm{~km}$
(d) $64 \mathrm{~km}$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 28, Problem 73

Instant Answer

Solved by Expert Hast Aggarwal

01/15/2022

Step 1

This is given by the formula for the distance to the horizon from a height h above a spherical Earth of radius R: \[d = \sqrt{2Rh + h^2}\] Show more…

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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 [AIEEE 2012] (a) $80 \mathrm{~km}$ (b) $16 \mathrm{~km}$ (c) $40 \mathrm{~km}$ (d) $64 \mathrm{~km}$

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Key Concepts

Line-of-Sight Distance Calculation

This concept involves determining the maximum distance over which an observer or sensor (such as a radar) can detect an object when both are on a curved surface. The calculation uses the relationship d = ?(2Rh), where d is the distance to the horizon, R is the radius of the Earth, and h is the height of the observer above ground level. This geometric approach is critical in understanding the limitations imposed by Earth’s curvature on signal or object detection.

Earth Curvature Impact

This concept focuses on how the curvature of the Earth limits the visibility or detection range of any elevated radar or optical system. Because the Earth curves away from an observer, there is a natural horizon beyond which objects cannot be seen due to the obstruction by the Earth itself. This principle is essential for accurately predicting detection ranges in various applications, including radar operation.

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