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

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$375$

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(C) The range $d$ of a $TV$ transmission tower of height $h$ is given by the formula $d = \sqrt{2Rh}$,where $R$ is the radius of the Earth.Let the initial height be $h_1 = 125\, m$ and the initial range be $d_1 = \sqrt{2Rh_1}$.We want to double the range,so the new range $d_2 = 2d_1$.Substituting the formula,we get $\sqrt{2Rh_2} = 2\sqrt{2Rh_1}$.Squaring both sides,we get $2Rh_2 = 4(2Rh_1)$,which simplifies to $h_2 = 4h_1$.Substituting the value of $h_1$,we get $h_2 = 4 	imes 125\, m = 500\, m$.The increase in height required is $\Delta h = h_2 - h_1 = 500\, m - 125\, m = 375\, m$.

The $TV$ transmission tower at a particular station has a height of $125\, m$. For doubling the coverage range,the height of the tower should be increased by .............$m$.

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