Question

The area to be covered for the T.V telecast is doubled then the height of the transmitting antenna will have to be:
A. Doubled
B. Halved
C. Quadrupled
D. Kept unchanged

Answer 1

Hint: To know the effect in height of transmitting antenna (TV tower) we will use formula $d=\sqrt{2Rh}$ which will give us the relation between area to be covered for TV telecast and height of transmitting antenna (TV tower).

Formula used:
$d=\sqrt{2Rh}$

Complete step by step solution:

As shown in the figure if total range of distance is d than area covered will be given by
$\begin{align}
  & \Rightarrow A=\pi {{d}^{2}} \\
 & \therefore A\propto {{d}^{2}}....\left( 1 \right) \\
\end{align}$
Now we know that relation between the height of the transmitting antenna (TV tower) and area covered by TV telecast can be given as
$d=\sqrt{2Rh}$
Where, d = maximum distance
h = height of antenna
R = radius of the earth
Taking square on both sides
${{d}^{2}}=2Rh.....\left( 2 \right)$
Now we can put the relation of equation (1) in equation (2) so that we will get
$A=2Rh$
Here the radius of the earth which is constant hence we can write above equation as
$A\propto h......\left( 3 \right)$

Now from equation (3) we can conclude that when the area (A) to be covered for TV telecast is doubled then the height of the transmitting antenna (h) also be doubled.

Hence, the option (A) doubled is correct.

Additional information:
Remote sensing:-
Remote sensing is a very useful method for observing or capturing or measuring the object at a certain distance it can be done by satellites.
Distance of the signals which can be received by the antenna is given by
$d=\sqrt{2hR}$
Where R = radius of the earth
h = height of the antenna.

Note:
As we gave in the question we have to consider the area of the TV telecast which gives the correct answer. But if we consider only distance (d) then it will lead us to incorrect answers.