On heating a liquid having coefficient of volume expension `alpha` in a container having coefficient of linear expansion `alpha//2,` the level of the liquid in the container would

Options

A. rise
B. fall
C. remains almost stationary
D. Cannot be bredicted

Explanation

To solve the problem, we need to analyze the effects of thermal expansion on both the liquid and the container when they are heated.

### Step-by-Step Solution:

1. **Identify the Coefficients of Expansion**:
- The coefficient of volume expansion of the liquid is given as \( \alpha \).
- The coefficient of linear expansion of the container is given as \( \frac{\alpha}{2} \).

2. **Relate Linear Expansion to Volume Expansion**:
- The volume expansion coefficient (\( \gamma \)) of a material is related to its linear expansion coefficient (\( \alpha \)) by the formula:
\[ \gamma = 3\alpha \quad \text{(for three-dimensional expansion)} \]
- For the container, since it has a linear expansion coefficient of \( \frac{\alpha}{2} \), the volume expansion coefficient of the container (\( \gamma_c \)) will be:
\[ \gamma_c = 3 \left(\frac{\alpha}{2}\right) = \frac{3\alpha}{2} \]

3. **Compare the Coefficients**:
- Now we compare the volume expansion coefficients:
- Liquid: \( \gamma_L = \alpha \)
- Container: \( \gamma_c = \frac{3\alpha}{2} \)
- Since \( \frac{3\alpha}{2} > \alpha \), the container expands more than the liquid when heated.

4. **Effect on Liquid Level**:
- Initially, assume the liquid fills the container to the top. As the container expands more than the liquid, the space available in the container increases more than the volume of the liquid.
- Therefore, the level of the liquid in the container will fall.

5. **Conclusion**:
- The level of the liquid in the container will decrease upon heating.

### Final Answer:
The level of the liquid in the container would **fall**.

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