Verified Solution • 2025–26 Session moderate

QJEEM21Phaf14: JEE Main 2021 Physics - Class 12 JEEM21Phaf14 Solution: If the sum of the heights of transmitting and receiving…

If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is ___________ km. (Take radius of Earth = 6400 km)

Step-by-Step Verified Solution

hT = hR = 160 ........ (i)

d=2RhT+2RhRd = \sqrt {2R{h_T}} + \sqrt {2R{h_R}}

d=2R[hT+hR]d = \sqrt {2R} \left[ {\sqrt {{h_T}} + \sqrt {{h_R}} } \right]

d=2R[x+160−x]d = \sqrt {2R} \left[ {\sqrt x + \sqrt {160 - x} } \right]

d(d)dx=0{{d(d)} \over {dx}} = 0

12x+1(−1)2160−x=0{1 \over {2\sqrt x }} + {{1( - 1)} \over {2\sqrt {160 - x} }} = 0

1x=1160−x{1 \over {\sqrt x }} = {1 \over {\sqrt {160 - x} }}

x = 80 m

dmax⁡=2×6400[801000+201000]{d_{\max }} = \sqrt {2 \times 6400} \left[ {\sqrt {{{80} \over {1000}}} + \sqrt {{{20} \over {1000}}} } \right]

=802×2801010= {{80\sqrt 2 \times 2\sqrt {80} } \over {10\sqrt {10} }}

=8×2×2×22=64= 8 \times 2 \times \sqrt 2 \times 2\sqrt 2 = 64 km

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring