Calculate the radius of a capillary tube, given the height of water rise and mercury depression, and their respective surface tensions and densities.

The height $h$ to which a liquid rises or falls in a capillary tube is given by:

$$h = \frac{2T \cos\theta}{r \rho g}$$

where $T$ is the surface tension, $\theta$ is the angle of contact, $r$ is the radius of the capillary tube, $\rho$ is the density of the liquid, and $g$ is the acceleration due to gravity.

For water (subscript 'w'):

• Height of rise, $h_w = 10 \text{ cm}$
• Density,