In a capillary tube experiment, a vertical 30 cm long capillary tube is dipped in water. The water rises up to a height of 10 cm due to capillary action. If this experiment is conducted in a freely falling elevator, the length of te water column becomes

Options

A. 30 cm
B. greater than 10 cm
C. equal to 10 cm
D. less than 10 cm

Answer

To solve the problem, we need to analyze the effect of capillary action in a normal scenario and then understand how it changes in a freely falling elevator.

### Step-by-Step Solution:

1. **Understanding Capillary Action**:
In a normal situation, when a capillary tube is dipped in water, the water rises due to surface tension. The height to which the water rises (h) is determined by the balance of forces: the upward surface tension force and the downward gravitational force acting on the weight of the water column.

2. **Given Data**:
- Length of the capillary tube (L) = 30 cm
- Height of water column in normal conditions (h) = 10 cm

3. **Weight of Water Column**:
The weight of the water column can be expressed as:
\[ W = \rho g V \]
where \( \rho \) is the density of water, \( g \) is the acceleration due to gravity, and \( V \) is the volume of the water column.

4. **Capillary Rise Equation**:
The height of the water column in the capillary tube is given by:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
where \( T \) is the surface tension, \( \theta \) is the contact angle, and \( r \) is the radius of the capillary tube.

5. **Effect of Free Fall**:
In a freely falling elevator, the effective gravitational force acting on the water column becomes zero (g = 0). This means that the downward force due to gravity is no longer acting on the water column.

6. **Resulting Forces in Free Fall**:
Since the gravitational force is zero, the only force acting on the water is the surface tension force. In this case, the water will rise to fill the entire capillary tube because there is no weight to counteract the surface tension.

7. **Final Height of Water Column**:
Therefore, in a freely falling elevator, the height of the water column will equal the length of the capillary tube:
\[ \text{Height of water column} = \text{Length of capillary tube} = 30 \text{ cm} \]

### Conclusion:
The water will rise to the full length of the capillary tube, which is 30 cm.

### Answer:
The length of the water column becomes **30 cm**.

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