If the range of a TV telecast is to be double | vedclass

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(C) The range $d$ of a transmitting antenna of height $h$ is given by the formula: $d = \sqrt{2Rh}$,where $R$ is the radius of the Earth.From this rel

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Quadrupled

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(C) The range $d$ of a transmitting antenna of height $h$ is given by the formula: $d = \sqrt{2Rh}$,where $R$ is the radius of the Earth.From this relation,we can see that $d \propto \sqrt{h}$.If the range is to be doubled,let the new range be $d' = 2d$ and the new height be $h'$.Then,$d' = \sqrt{2Rh'} \implies 2d = \sqrt{2Rh'}$.Squaring both sides,we get $4d^2 = 2Rh'$.Since $d^2 = 2Rh$,we substitute this into the equation: $4(2Rh) = 2Rh'$.$8Rh = 2Rh' \implies h' = 4h$.Therefore,the height of the transmitting antenna must be quadrupled.

If the range of a $TV$ telecast is to be doubled,the height of the transmitting antenna must be:

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