Question

Capillary W contains water and capillary M contains mercury. The contact angles between the capillary wall and the edge of the meniscus at the air-liquid interface in $W$ and $M$ are $\theta_W$ and $\theta_M$, respectively. The contact angles satisfy the conditions

• A. $\theta_W$ > 90° and $\theta_M$ > 90°
• B. $\theta_W$ > 90° and $\theta_M$ < 90°
• C. $\theta_W$ < 90° and $\theta_M$ > 90°
• D. $\theta_W$ < 90° and $\theta_M$ < 90°

Answer 1

The Correct Option is C

The question revolves around the concept of contact angles in capillarity involving water and mercury. When dealing with capillary action, the contact angle is crucial as it helps determine whether a liquid will rise or fall in a tube.

1. Understanding Contact Angles:
   • The contact angle, denoted as \(\theta\), is the angle formed between the surface of a liquid and the surface of a solid.
   • If \(\theta < 90^\circ\), the liquid wets the surface, causing capillary rise.
   • If \(\theta > 90^\circ\), the liquid does not wet the surface, causing capillary depression.
2. Capillary Action with Water and Mercury:
   • Water typically wets glass, resulting in a contact angle of less than \(90^\circ\).
   • Mercury, on the other hand, does not wet glass, leading to a contact angle greater than \(90^\circ\).
3. Analyzing Given Options:
   • Option: \(\theta_W > 90^\circ\) and \(\theta_M > 90^\circ\): Incorrect because water should have a contact angle less than 90°.
   • Option: \(\theta_W > 90^\circ\) and \(\theta_M < 90^\circ\): Incorrect because mercury should have a contact angle greater than 90°.
   • Option: \(\theta_W < 90^\circ\) and \(\theta_M > 90^\circ\): Correct, as it matches the behavior of water and mercury in glass.
   • Option: \(\theta_W < 90^\circ\) and \(\theta_M < 90^\circ\): Incorrect because mercury should have a contact angle greater than 90°.
4. Conclusion:
   • The correct configuration corresponds to water having a contact angle less than 90 degrees and mercury having a contact angle greater than 90 degrees.
   • Thus, the correct answer is: \(\theta_W < 90^\circ\) and \(\theta_M > 90^\circ\).