Question

A radar of power $1\ \text{kW}$ operating at frequency $10\ \text{GHz}$ is located on a mountain top of height $500\ \text{m}$. The maximum distance upto which it can detect object located on the surface of the earth is $\left[\text{Radius of earth} = 6.4 \times 10^6\ \text{m}\right]$

• A. $8\ \text{km}$
• B. $80\ \text{km}$
• C. $70\ \text{km}$
• D. $56\ \text{km}$

Hint:

Radar range depends on height due to curvature of the earth, not on radar power.

Answer 1

The Correct Option is B

Step 1: Use line-of-sight distance formula.
The maximum distance upto which radar can detect an object is given by: \[ d = \sqrt{2Rh} \] Step 2: Substitute given values.
\[ R = 6.4 \times 10^6\ \text{m}, \quad h = 500\ \text{m} \] Step 3: Calculate distance.
\[ d = \sqrt{2 \times 6.4 \times 10^6 \times 500} \] Step 4: Simplify.
\[ d = \sqrt{6.4 \times 10^9} \approx 8 \times 10^4\ \text{m} = 80\ \text{km} \]