Question

The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased by

• A. 125 m
• B. 250 m
• C. 375 m
• D. 500 m

Answer 1

Answer: (C)

375 m

Answer 2

The correct answer is (C) : 375
Let's consider H' as the antenna's new height.
As the range of antenna , $d = \sqrt{2RH}$
Hence , d1 = d = $\sqrt{2×R×125}$ ……… (i)
d2 = 2d = $\sqrt{2×R×H'}$ ……….. (ii)
By dividing (i) and (ii) , we get
$\frac{d}{2d}=\sqrt{\frac{125}{H'}}$
Then , squaring the above equation , we get
$\frac{1}{4}=\frac{125}{H'}$
H' = 500 m
∴ Increase in height = H' - H
= 500 - 125
= 375 m