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

We need to find the increase in height required to double the coverage range of a TV tower. The range of a TV transmission tower is $$d = \sqrt{2Rh}$$ where R is the radius of Earth and h is the height of the tower.

The original range is $$d_1 = \sqrt{2R \times 125}$$ when the tower height is 125 m, and the new range is $$d_2 = 2d_1 = \sqrt{2Rh_2}$$. Equating these gives $$2\sqrt{2R \times 125} = \sqrt{2Rh_2}$$, and squaring both sides yields $$4 \times 2R \times 125 = 2Rh_2$$. Therefore, $$h_2 = 4 \times 125 = 500 \text{ m}$$.

Hence the required increase in height is $$\Delta h = h_2 - h_1 = 500 - 125 = 375 \text{ m}$$. The answer is Option B: 375 m.