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(C) The covering range $d$ of a $TV$ transmission tower of height $h$ is given by the formula $d = \sqrt{2hR}$,where $R$ is the radius of the Earth.Fr

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$4$

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(C) The covering range $d$ of a $TV$ transmission tower of height $h$ is given by the formula $d = \sqrt{2hR}$,where $R$ is the radius of the Earth.From this relation,we can see that $d \propto \sqrt{h}$.Let the initial range be $d_1 = \sqrt{2h_1R}$ and the new range be $d_2 = \sqrt{2h_2R}$.We want the new range to be double the initial range,so $d_2 = 2d_1$.Substituting the expressions,we get $\sqrt{2h_2R} = 2 \sqrt{2h_1R}$.Squaring both sides,we get $2h_2R = 4(2h_1R)$.This simplifies to $h_2 = 4h_1$.Therefore,the height of the tower must be multiplied by $4$ to double the covering range.

To double the covering range of a $TV$ transmission tower,its height should be multiplied by

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