A T.V. tower has a height of 200 m. By how much the height of tower be increased to make the coverage range four times?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3000 m
A TV signal travels in a straight line, so the coverage range of a tower of height h is \( d = \sqrt{2Rh} \), where R is the radius of the earth. For the same R, \( d\propto\sqrt{h} \).
\( \displaystyle \frac{d_2}{d_1} = \sqrt{\frac{h_2}{h_1}} = 4 \Rightarrow \frac{h_2}{h_1} = 16 \)
\( h_2 = 16\times200\,\mathrm{m} = 3200\,\mathrm{m} \)
The question asks for the increase in height.
\( \Delta h = h_2 - h_1 = 3200 - 200 = 3000\,\mathrm{m} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Space Wave – “… If the transmitting antenna is at a height hT, then you can show that the distance to the horizon dT is given as
\( \displaystyle d_T = \sqrt{2Rh_T} \)
, where R is the radius of the earth (approximately 6400 km).”