Option D, "Statement I is true but Statement II is false," is the correct choice. Here's an explanation for both statements:

Statement I: True

The contact angle between a solid and a liquid is indeed a measure of the wettability of the solid surface by the liquid. The contact angle is determined by the nature of both the solid and the liquid. It is a function of the interfacial tensions between solid-liquid ($ \gamma_{\text{SL}} $), solid-vapor ($ \gamma_{\text{SV}} $), and liquid-vapor ($ \gamma_{\text{LV}} $). This relationship can be understood through Young's equation:

$ \cos \theta = \frac{\gamma_{\text{SV}} - \gamma_{\text{SL}}}{\gamma_{\text{LV}}} $

Where $ \theta $ is the contact angle. Therefore, since the interfacial tensions vary with the materials in contact, the contact angle is indeed a property of the materials of both the solid and the liquid.

Statement II: False

The rise of a liquid in a capillary tube is strongly dependent on the inner radius of the tube. This relationship is described by the Jurin's Law, which states the height ($ h $) to which a liquid will rise (or fall) in a capillary tube is inversely proportional to the radius ($ r $) of the tube, among other factors. The law is given by:

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

Where:

• $ \gamma $ is the liquid-air surface tension,
• $ \theta $ is the contact angle,
• $ \rho $ is the density of the liquid,
• $ g $ is the acceleration due to gravity,
• $ r $ is the radius of the capillary tube.

As seen from the equation, $ h $ is inversely proportional to $ r $. Therefore, the rise of the liquid indeed depends on the inner radius of the tube, making Statement II false.