QJEEM24Ph47b2: JEE Main 2024 Physics - Class 11 JEEM24Ph47b2 Solution: Given below are two statements : Statement I : The contact…

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.