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The lower end of a capillary tube touche...

The lower end of a capillary tube touches a liquid whose angle of contact is `110^(@)`, the liquid .

A

rises into the tube

B

falls in the tube

C

may rise or fall inside

D

neither rises nor falls inside the tube

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the situation of a capillary tube in contact with a liquid that has an angle of contact of \(110^\circ\). The angle of contact affects whether the liquid will rise or fall in the capillary tube. ### Step-by-Step Solution: 1. **Understanding Capillarity**: - Capillary action occurs due to the adhesive and cohesive forces between the liquid molecules and the molecules of the tube. The angle of contact (or wetting angle) determines the behavior of the liquid in the capillary tube. 2. **Identify the Angle of Contact**: - The angle of contact given is \(110^\circ\). This is obtuse, which indicates that the liquid does not wet the surface of the tube well. 3. **Determine the Behavior of the Liquid**: - For a liquid to rise in a capillary tube, the angle of contact should be acute (less than \(90^\circ\)). In this case, since the angle is \(110^\circ\), the liquid will not rise in the tube. 4. **Using the Capillary Rise Formula**: - The height \(h\) to which a liquid rises in a capillary tube can be calculated using the formula: \[ h = \frac{2T \cos \theta}{\rho g R} \] - Here, \(T\) is the surface tension of the liquid, \(\theta\) is the angle of contact, \(\rho\) is the density of the liquid, \(g\) is the acceleration due to gravity, and \(R\) is the radius of the capillary tube. 5. **Substituting the Angle of Contact**: - Since the angle of contact is \(110^\circ\), we need to find \(\cos(110^\circ)\). - The value of \(\cos(110^\circ)\) is negative, which indicates that the height \(h\) will also be negative. 6. **Conclusion**: - A negative height means that the liquid will fall in the capillary tube rather than rise. Therefore, the correct answer is that the liquid will fall into the tube. ### Final Answer: The liquid will fall into the capillary tube.
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