If a liquid rises to the same height in two capillaries of the same material at the same temperature, then

Options

A. the weight of liquid in both capillaries must be equal
B. the radius of meniscus must be equal
C. the capillaries must be cylindrical and vertical
D. the hydrostatic pressure at the base of capillaries must be same

Explanation

To solve the problem, we need to analyze the conditions given in the question regarding the behavior of a liquid in two capillaries of the same material at the same temperature.

### Step-by-Step Solution:

1. **Understanding Capillarity**:
The height to which a liquid rises in a capillary tube is given by the formula:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
where:
- \( h \) = height of the liquid column,
- \( T \) = surface tension of the liquid,
- \( \theta \) = angle of contact,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity,
- \( r \) = radius of the capillary tube.

2. **Given Conditions**:
According to the problem, the height \( h \) is the same in both capillaries. Since the capillaries are made of the same material and are at the same temperature, we can assume that:
- The surface tension \( T \) is the same,
- The angle of contact \( \theta \) is the same,
- The density \( \rho \) is the same,
- The acceleration due to gravity \( g \) is constant.

3. **Equating the Heights**:
Since the height \( h \) is the same for both capillaries, we can set up the following equation:
\[ \frac{2T \cos \theta}{\rho g r_1} = \frac{2T \cos \theta}{\rho g r_2} \]
This implies that:
\[ r_1 = r_2 \]
Therefore, the radii of the two capillaries must be equal.

4. **Weight of the Liquid Column**:
The weight of the liquid column in each capillary can be expressed as:
\[ W = \rho V g = \rho \pi r^2 h g \]
Since \( h \), \( \rho \), and \( r \) are the same for both capillaries, the weights of the liquid columns must also be equal.

5. **Conclusion**:
From the analysis, we conclude that:
- The radii of both capillaries must be equal.
- The weights of the liquid columns in both capillaries are equal.

Thus, the correct options based on the analysis are:
- The radii of the capillaries are equal.
- The weights of the liquid columns are equal.

### Final Answer:
- The radii of the capillaries are equal.
- The weights of the liquid columns are equal.