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(D) The coverage range $d$ of a $TV$ antenna of height $h$ is given by the formula $d = \sqrt{2Rh}$,where $R$ is the radius of the Earth.
From this,w

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$300$

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(D) The coverage range $d$ of a $TV$ antenna of height $h$ is given by the formula $d = \sqrt{2Rh}$,where $R$ is the radius of the Earth.
From this,we can see that $d \propto \sqrt{h}$.
Let the initial height be $h_1 = 100 \, m$ and the initial range be $d_1$.
We want the new range $d_2 = 2d_1$.
Since $d \propto \sqrt{h}$,we have $\frac{d_2}{d_1} = \sqrt{\frac{h_2}{h_1}}$.
Substituting the values: $2 = \sqrt{\frac{h_2}{100}}$.
Squaring both sides: $4 = \frac{h_2}{100}$,which gives $h_2 = 400 \, m$.
The increase in height required is $\Delta h = h_2 - h_1 = 400 \, m - 100 \, m = 300 \, m$.

$A$ $TV$ transmission antenna at a particular station has a height of $100 \, m$. By how much should the height of the antenna be increased to double its coverage range (in $m$)?

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