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?
Answer & explanation
Correct answer: option 4
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,
$d∝\sqrt{h}$
$∴\frac{d_2}{d_1}=\sqrt{\frac{h_2}{h_1}}$
$16=\frac{h_2}{h_1}$
$⇒h_2=h_1×16$
$=16×200=3200m$
$Δh=h_2-h_1=3200-200=3000m$