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JEE Main 201910 JanuaryMorning Shift

Exam: JEE Main
Year: 2019
Date: 10 January
Shift: Morning Shift
Subject: Physics
Chapter: Communication System

JEE Main 2019 · 10 January · Morning Shift · Physics · Communication System

A TV transmission tower has a height of 140m and the height of the...

A TV transmission tower has a height of

140m

and the height of the receiving antenna is

40m .

What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given: radius of earth

= 6.4 \times {10}^{6}m ) .

Options

A $48km$
B $40km$
C $80km$
D $65km$

Correct answer

D. $65km$

Step-by-step solution

D = \sqrt{2{h}_{T}R} + \sqrt{2{h}_{R}R}

D = \sqrt{2 \times 140 \times 64 \times {10}^{5}} + \sqrt{2 \times 40 \times 64 \times {10}^{5}}

D = 8 \times {10}^{3} [ \sqrt{28} + \sqrt{8} ]

D = 8 \times {10}^{3} [ 2\sqrt{7} + 2\sqrt{2} ]

D = 16 \times {10}^{3} [ \sqrt{7 + \sqrt{2}} ]

D = 16 \times {10}^{3}\left[2.6 + 1.4\right]

= 64000m = 64km ≃ 65km

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