Question:
If the height of TV tower is increased by $21\%$, the transmission range is enhanced by
If the height of TV tower is increased by $21\%$, the transmission range is enhanced by
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Range $\propto \sqrt{h}$ → percentage change halves approximately.
Updated On: May 2, 2026
- $10\%$
- $5\%$
- $15\%$
- $25\%$
- $12\%$
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The Correct Option is A
Solution and Explanation
Concept: Range of TV transmission
The maximum range of transmission is: \[ d = \sqrt{2Rh} \] Thus: \[ d \propto \sqrt{h} \] ---
Step 1: Apply proportionality \[ d \propto \sqrt{h} \Rightarrow \frac{d_2}{d_1} = \sqrt{\frac{h_2}{h_1}} \] ---
Step 2: Increase in height \[ h_2 = 1.21h_1 \] ---
Step 3: Calculate new range \[ \frac{d_2}{d_1} = \sqrt{1.21} = 1.1 \] ---
Step 4: Percentage increase \[ \% \text{ increase} = (1.1 - 1)\times 100 = 10\% \] --- Physical Insight:
• Range increases slowly with height
• Doubling height does not double range --- Final Answer: \[ \boxed{10\%} \]
The maximum range of transmission is: \[ d = \sqrt{2Rh} \] Thus: \[ d \propto \sqrt{h} \] ---
Step 1: Apply proportionality \[ d \propto \sqrt{h} \Rightarrow \frac{d_2}{d_1} = \sqrt{\frac{h_2}{h_1}} \] ---
Step 2: Increase in height \[ h_2 = 1.21h_1 \] ---
Step 3: Calculate new range \[ \frac{d_2}{d_1} = \sqrt{1.21} = 1.1 \] ---
Step 4: Percentage increase \[ \% \text{ increase} = (1.1 - 1)\times 100 = 10\% \] --- Physical Insight:
• Range increases slowly with height
• Doubling height does not double range --- Final Answer: \[ \boxed{10\%} \]
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