Q 12-08-139JEE MainJEE Main 2022 (27 Jun, Shift 1)Medium
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 $K\sqrt5\times10^2$ m. The value of $K$ is ______ .
(Assume radius of Earth is $64\times10^5$ m) [Calculate upto nearest integer value]
Numerical value type. Enter your answer.
Answer: 192
$$d_{\max} = \sqrt{2Rh_T} + \sqrt{2Rh_R}$$
$\sqrt{2(64\times10^5)(25)} = \sqrt{32\times10^7} = 8000\sqrt5$ m
$\sqrt{2(64\times10^5)(49)} = 7\sqrt{128\times10^5} = 7\times1600\sqrt5 = 11200\sqrt5$ m
$$d_{\max} = 19200\sqrt5\ \text{m} = 192\sqrt5\times10^2\ \text{m}$$
$K = 192$.
Solution by Sreeraj P, M.Sc Physics