If a liquid neither rises nor depresses in a capillary then it means that

Options

A. angle of contact is `0^(@)`
B. angle of contact may by `90^(@)`
C. surface tension of the liquid must be zero
D. None of these

Answer

To solve the question "If a liquid neither rises nor depresses in a capillary, then it means that...", we need to analyze the factors that affect the behavior of liquids in capillary tubes.

### Step-by-Step Solution:

1. **Understanding Capillarity**:
- Capillarity is the ability of a liquid to flow in narrow spaces without the assistance of external forces. This phenomenon is influenced by surface tension, adhesive forces between the liquid and the walls of the capillary, and cohesive forces within the liquid.

2. **Capillary Rise Formula**:
- The height (h) to which a liquid rises or is depressed in a capillary tube can be described by the formula:
\[ h = \frac{2s \cos \theta}{r \rho g} \]
- Where:
- \( s \) = surface tension of the liquid
- \( \theta \) = angle of contact (wetting angle)
- \( r \) = radius of the capillary tube
- \( \rho \) = density of the liquid
- \( g \) = acceleration due to gravity

3. **Analyzing the Condition of No Rise or Depression**:
- If the liquid neither rises nor depresses, it implies that the height \( h \) is equal to zero.
- For \( h \) to be zero, the numerator \( 2s \cos \theta \) must be zero or the denominator must be infinitely large.

4. **Evaluating the Factors**:
- The radius \( r \) of the capillary tube cannot be infinitely large, as it is a physical quantity.
- The density \( \rho \) of the liquid also cannot be infinitely large.
- Therefore, the only way for the numerator \( 2s \cos \theta \) to equal zero is if \( \cos \theta = 0 \), which occurs when \( \theta = 90^\circ \).

5. **Conclusion**:
- Thus, if a liquid neither rises nor depresses in a capillary tube, it indicates that the angle of contact \( \theta \) is approximately \( 90^\circ \). This means that the liquid does not wet the surface of the capillary tube.

### Final Answer:
If a liquid neither rises nor depresses in a capillary tube, it means that the angle of contact between the liquid and the wall of the tube is approximately \( 90^\circ \).

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