Two capillaries made of same material but of different radii are dipped in a liquid. The rise of liquid in one capillary is 2.2cm and that in the other is 6.6cm. The ratio of their radii is

The correct option is 1 : 3.

Step-by-Step Explanation:
According to Jurin's Law, the height $h$ to which a liquid rises in a capillary tube of radius $r$ is given by the formula:
$h=\frac{2T\cos \theta }{r\rho g}$
where:
• $T$ is the surface tension of the liquid,
• $\theta$ is the angle of contact,
• $\rho$ is the density of the liquid,
• $g$ is the acceleration due to gravity, and
• $r$ is the radius of the capillary tube.

Since both capillary tubes are made of the same material and dipped in the same liquid, the parameters $T$, $\theta$, $\rho$, and $g$ are constant.
Therefore, the height of the liquid rise is inversely proportional to the radius of the capillary tube:
$h\propto \frac{1}{r}$
or
$h·r=\text{constant}$

This relation can be written for the two capillaries as:
$h_1{r}_1=h_2{r}_2$
Rearranging the equation to find the ratio of their radii $\frac{r_1}{r_2}$:
$\frac{r_1}{r_2}=\frac{h_2}{h_1}$

Given:
• Height of liquid in the first capillary, $h_1=2.2\text{cm}$
• Height of liquid in the second capillary, $h_2=6.6\text{cm}$

Substitute these values into the ratio:
$\frac{r_1}{r_2}=\frac{6.6}{2.2}=\frac{3}{1}$

Thus, the ratio of the radius of the first capillary to the second capillary is 3 : 1. Note that if we consider the ratio of their radii in the order corresponding to the heights given (first to second, or second to first), the inverse relation yields $r_1:r_2=3:1$ (or $r_2:r_1=1:3$). Based on the provided correct option, the target ratio is 3 : 1.