JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Semiconductors

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by

21%

Answer: (C)

Solution

The transmission range of a TV tower is

R = 2 R h

, where

R

is Earth's radius and

h

is tower height.

Initially:

R_{1} = 2 R h_{1}

After 21% increase:

h_{2} = 1.21 h_{1}

New range:

R_{2} = 2 R (1.21 h_{1}) = 1.21 \cdot 2 R h_{1} = 1.1 R_{1}

Percentage increase =

\frac{R _{2} - R _{1}}{R _{1}} \times 100 = (1.1 - 1) \times 100 = 10%

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Single correct option