A T.V tower has a height of 200 m. By how much the height of tower be increased to make the coverage range four times?

3000 m

The correct answer is Option (4) → 3000 m

The coverage range (d) of a tower is given by -

$d=\sqrt{2Rh}$

where,

$R=6.4×10^6m$

h = height of tv tower ($h_1=200m$)

if the coverage range is increased four times,

$d_2=4d_1$

and,

$d∝\sqrt{h}$

$∴\frac{d_2}{d_1}=\sqrt{\frac{h_2}{h_1}}$

$16=\frac{h_2}{h_1}$

$⇒h_2=h_1×16$

$=16×200=3200m$

$Δh=h_2-h_1=3200-200=3000m$