JEE Main · 2021 · 18 Mar 2021 · Shift 2 · EM Waves

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A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at
(i) ground level
(ii) a height of 5 m

The increase in the antenna range in case (ii) relative to case (i) is

n %

.
The value of n, to the nearest integer, is ____

Answer: 50

Solution

An antenna at height

h

above an earth of radius

R

sees as far as its horizon,

d = 2 R h

. With the receiver on the ground the usable range is that of the tower alone,

d_{1} = 2 R (20)

. Raising the receiver to

5

m adds its own horizon distance, so

d_{2} = 2 R (20) + 2 R (5)

. The fractional increase is

\frac{d _{2} - d _{1}}{d _{1}} = \frac{2 R ( 5 )}{2 R ( 20 )} = \frac{5}{20} = \frac{1}{2}

so the range grows by

50

per cent and

n = 50

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Numerical answer

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