Question:
A TV tower has a height of 100m. To double the coverage distance of the tower, the height of the tower must be increased by:
A TV tower has a height of 100m. To double the coverage distance of the tower, the height of the tower must be increased by:
Show Hint
To double the range, you need four times the height ($h \propto d^2$).
Updated On: Jun 6, 2026
- 200 m
- 300 m
- 400 m
- 100 m
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Coverage distance of a TV tower $d = \sqrt{2Rh}$.
Step 2: Meaning
The distance $d$ is proportional to $\sqrt{h}$.
Step 3: Analysis
$d_1 = \sqrt{2Rh_1}$, $d_2 = 2d_1 = \sqrt{2Rh_2}$. $\sqrt{2Rh_2} = 2\sqrt{2Rh_1} \rightarrow h_2 = 4h_1 = 4(100) = 400$ m. The increase in height is $h_2 - h_1 = 400 - 100 = 300$ m.
Step 4: Conclusion
The height must be increased by 300 m.
Final Answer: (B)
Coverage distance of a TV tower $d = \sqrt{2Rh}$.
Step 2: Meaning
The distance $d$ is proportional to $\sqrt{h}$.
Step 3: Analysis
$d_1 = \sqrt{2Rh_1}$, $d_2 = 2d_1 = \sqrt{2Rh_2}$. $\sqrt{2Rh_2} = 2\sqrt{2Rh_1} \rightarrow h_2 = 4h_1 = 4(100) = 400$ m. The increase in height is $h_2 - h_1 = 400 - 100 = 300$ m.
Step 4: Conclusion
The height must be increased by 300 m.
Final Answer: (B)
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