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← JEE Main 2022 · 27 Jun · Shift 1
PhysicsInteger+4 / -1Question 58 of 90

JEE Main 2022 · 27 Jun · Shift 1, Physics question 58

The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is K5×102K\sqrt5\times10^2 m. The value of K is ______.

(Assume radius of Earth is 64×10+564\times10^{+5} m) [Calculate upto nearest integer value]

Answer and worked solution

Official answer: 192

LOS range. 2Rh1+2Rh2\sqrt{2Rh_1}+\sqrt{2Rh_2} with 2R=1.28×107=16005\sqrt{2R}=\sqrt{1.28\times10^7}=1600\sqrt5.

Sum. 16005(5+7)=192005=1925×1021600\sqrt5(5+7)=19200\sqrt5=192\sqrt5\times10^2 m.

Answer: 192