If a capillary tube is dipped and the liquid levels inside and outside the tube are same. Then the angle of contact is

Options

A. zero
B. `90^(@)`
C. `45^(@)`
D. Cannot be obtained

Explanation

To solve the problem, we need to determine the angle of contact (θ) when a capillary tube is dipped in a liquid and the liquid levels inside and outside the tube are the same.

### Step-by-Step Solution:

1. **Understanding Capillary Action**:
- Capillary action occurs when a liquid rises or falls in a narrow tube due to the balance between cohesive and adhesive forces. The height (h) of the liquid column in the capillary tube is given by the formula:
\[ h = \frac{2s \cos \theta}{r \rho g} \]
where:
- \( s \) = surface tension of the liquid,
- \( \theta \) = angle of contact,
- \( r \) = radius of the capillary tube,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity.

2. **Setting the Condition**:
- The problem states that the liquid levels inside and outside the tube are the same, which implies that there is no rise (or fall) of liquid in the tube. Therefore, the height \( h \) is equal to 0.

3. **Substituting into the Formula**:
- Since \( h = 0 \), we can substitute this into the capillary rise formula:
\[ 0 = \frac{2s \cos \theta}{r \rho g} \]

4. **Analyzing the Equation**:
- For the equation to hold true (i.e., equal to zero), the numerator must be zero because the denominator (which consists of \( r \), \( \rho \), and \( g \)) cannot be zero. Thus, we have:
\[ 2s \cos \theta = 0 \]

5. **Solving for θ**:
- Since the surface tension \( s \) is a positive value for any liquid, we can conclude:
\[ \cos \theta = 0 \]
- The angle \( \theta \) for which the cosine is zero is:
\[ \theta = 90^\circ \]

6. **Conclusion**:
- Therefore, the angle of contact when the liquid levels inside and outside the capillary tube are the same is \( 90^\circ \).

### Final Answer:
The angle of contact \( \theta \) is \( 90^\circ \).

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