Given below are two statements :
Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
In the light of the above statements, choose the correct answer from the options given below :
Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
In the light of the above statements, choose the correct answer from the options given below :
- Both Statement I and Statement II are false
- Statement I is false but Statement II is true.
- Statement I is true but Statement II is false.
- Both Statement I and Statement II are true.
The Correct Option is C
Approach Solution - 1
Statement I: This statement is correct. The contact angle between a solid and a liquid depends on the cohesive and adhesive forces, which are properties of the materials involved.
Statement II: This statement is incorrect. The height of liquid rise in a capillary tube is given by:
\[ h = \frac{2T \cos \theta}{\rho g r}, \] where T is the surface tension, θ is the contact angle, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the capillary tube. This equation shows that the height h is inversely proportional to the radius r of the tube, indicating that the rise does depend on the inner radius.
Hence, option (3) is correct.
Approach Solution -2
Statement I says: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
This statement is true because the contact angle depends on the molecular interactions between the solid surface and the liquid. Different combinations of solid and liquid materials produce different contact angles due to variations in surface tension and adhesive forces.
Step 2: Analyze Statement II.
Statement II says: The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
This statement is false because the height of capillary rise (or depression) is inversely proportional to the radius of the tube, as given by the formula: \[ h = \frac{2T \cos \theta}{\rho g r} \] where \(T\) is surface tension, \(\theta\) is the contact angle, \(\rho\) is the density, \(g\) is acceleration due to gravity, and \(r\) is the inner radius of the tube. Hence, smaller radius results in a higher rise of the liquid.
Step 3: Conclusion.
Statement I is true but Statement II is false.
\[ \boxed{\text{Statement I is true but Statement II is false.}} \]
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