Question

If the height of the tower used for L.D.S is increased by 21% then percentage change in range is?

• A. 10%
• B. 21%
• C. 19%
• D. 42%

Answer 1

The Correct Option is A

To solve this problem, we need to understand the relationship between the height of a tower and the range of a Line of Sight (L.D.S) communication. The range, \(R\), in this context is approximately proportional to the square root of the height, \(H\), of the tower: \(R \propto \sqrt{H}\).

When the height of the tower is increased by 21%, the new height, \(H_{\text{new}}\), becomes:

\(H_{\text{new}} = H + 0.21H = 1.21H\)

To find the new range, we use the proportional relationship:

\(R_{\text{new}} \propto \sqrt{H_{\text{new}}} = \sqrt{1.21H} = \sqrt{1.21}\cdot\sqrt{H}\)

The square root of 1.21 can be calculated as:

\(\sqrt{1.21} \approx 1.1\)

Thus, the new range is:

\(R_{\text{new}} \approx 1.1 \cdot \sqrt{H}\)

The percentage change in range can be calculated as follows:

\(\text{Percentage change} = \left(\frac{R_{\text{new}} - R_{\text{old}}}{R_{\text{old}}}\right) \times 100\%\)

Since \(R_{\text{old}} \propto \sqrt{H}\), by substitution we get:

\(\text{Percentage change} = \left(\frac{1.1 \sqrt{H} - \sqrt{H}}{\sqrt{H}}\right) \times 100\%\)

This simplifies to:

\(\left(1.1 - 1\right) \times 100\% = 0.1 \times 100\% = 10\%\)

Therefore, the percentage change in range is 10%.

Thus, the correct answer is 10%.