In a surface tension experiment with a capillary tube water rises upto `0.1m`. If the same experiment is repeated in an artificial satellite, which is revolving around the earth, water will rise in the capillary tube upto a height of

Options

A. `0.1m`
B. `0.2m`
C. `0.98m`
D. Full length of tube

Explanation

To solve the problem, we need to analyze the situation of water rising in a capillary tube both on Earth and in an artificial satellite.

### Step-by-Step Solution:

1. **Understand Capillary Action**:
- Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. It is influenced by surface tension, the density of the liquid, and the gravitational force acting on it.

2. **Given Data**:
- On Earth, the height to which water rises in the capillary tube is given as \( h = 0.1 \, \text{m} \).

3. **Capillary Rise Formula**:
- The height of the liquid column in a capillary tube can be expressed using the formula:
\[ h = \frac{2T}{\rho g r} \]
where:
- \( T \) = surface tension of the liquid,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity,
- \( r \) = radius of the capillary tube.

4. **Consider the Situation in an Artificial Satellite**:
- In an artificial satellite, the effective gravitational acceleration \( g \) is approximately zero because the satellite is in free fall, creating a microgravity environment.

5. **Effect of Zero Gravity**:
- If \( g = 0 \), the formula for capillary rise becomes:
\[ h = \frac{2T}{\rho \cdot 0 \cdot r} \]
This expression becomes undefined (or theoretically infinite) because we cannot divide by zero.

6. **Practical Limitation**:
- However, in reality, the water cannot rise indefinitely. The height to which the water can rise is limited by the physical length of the capillary tube itself.

7. **Conclusion**:
- Therefore, in an artificial satellite, the water will rise to the maximum height allowed by the capillary tube, which is equal to the length of the tube.

### Final Answer:
- The water will rise in the capillary tube up to the full length of the tube.

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