Question

The following statements are made with respect to capillaries and factors affecting it
A. Capillaries are directly proportional to surface tension
B. Capillaries are inversely proportional to density of liquid
C. Capillaries are directly proportional to diameter of the tube
D. Capillaries are inversely proportional to surface tension
E. Capillaries are directly proportional to density of liquid
Choose the correct answer from the options given below:

• A. A and C only
• B. A and B only
• C. B and C only
• D. D and E only

Hint:

Jurin's Law: $h = \frac{4\sigma\cos\theta}{\rho g d}$. Directly with $\sigma$, inversely with $\rho$ and $d$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Capillary rise/depression in a narrow cylindrical tube is governed by Jurin's law of surface tension and hydrostatic balance.
Key Formula or Approach:
\[ h = \frac{4\sigma \cos \theta}{\rho g d} \]
where \(\sigma\) is surface tension, \(\theta\) is contact angle, \(\rho\) is liquid density, and \(d\) is tube diameter.

Step 2: Detailed Explanation:
From Jurin's equation for capillary rise:
1. Surface Tension (A): Height \(h\) is directly proportional to surface tension \(\sigma\) (\(h \propto \sigma\)). Statement A is true.
2. Liquid Density (B): Height \(h\) is inversely proportional to density \(\rho\) (\(h \propto 1/\rho\)). Statement B is true.
3. Tube Diameter (C): Height \(h\) is inversely proportional to diameter \(d\) (\(h \propto 1/d\)). Statement C is false.
Thus, statements A and B only are correct.

Step 3: Final Answer:
Therefore, the correct answer is A and B only, corresponding to option (B).