Question

water rises to a height h when a capillary of radius r is dipped in water .for another capilllary of radius 2r dipped in water , it rises to the height

Answer 1

Question 36966

One might use Jurin's law in order to solve the problem. According to this law, liquid's height within a thin capillary tube is $h = \frac{2\gamma\cos\theta}{r\rho g}$ , where $\gamma$ is the liquid surface tension, $\theta$ is the contact angle of the liquid on the tube wall, $r$ is the tube radius and $\rho$ is the liquid density.

Replacing $r \to 2r$ , obtain $h' = \frac{2\gamma\cos\theta}{2r\rho g} = \frac{\gamma\cos\theta}{r\rho g} = \frac{h}{2}$ , hence for capillary of double radius, the water rises to the half of the height in the previous case.