The ratio of the rate of flow of water through pipes varies inversely, as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes of diameter 2 cm and 4 cm?

4 : 1

The correct answer is Option (4) → 4 : 1

The rate of flow varies inversely as the square of the radius.

Given:

• Diameters: 2 cm and 4 cm
• Radii: $r_1 = 1$ cm, $r_2 = 2$ cm

Since

$\text{Rate} \propto \frac{1}{r^2}$

$\text{Ratio of rates} = \frac{1}{1^2} : \frac{1}{2^2} = 1 : \frac{1}{4}$

Multiply both terms by 4:

$= 4 : 1$

Correct answer: 4 : 1