If the height of the TV tower is increased by 21%, then by what percentage will the transmission range of the tower be affected?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10%
The range of a TV tower of height h is the distance to the horizon, \( d = \sqrt{2Rh} \), where R is the radius of the earth. Hence \( d\propto\sqrt{h} \).
\( h' = 1.21\,h \)
\( \displaystyle \frac{d'}{d} = \sqrt{\frac{h'}{h}} = \sqrt{1.21} = 1.1 \)
The range becomes 1.1 times the original, an increase of 10%.
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 \( h_T \), then you can show that the distance to the horizon \( d_T \) is given as \( d_T = \sqrt{2Rh_T} \), where R is the radius of the earth (approximately 6400 km). \( d_T \) is also called the radio horizon of the transmitting antenna.”