Chosse the correct statement (s) about the pressure in a liquid .

Options

A. Two points in the same horizontal plane can not have te same pressure
B. Two points at different levels may have same pressure
C. two points at different levels canot have same pressure
D. Two points in the same vertical line always have different pressures

Answer

To solve the question regarding the pressure in a liquid, we need to analyze each of the four statements provided and determine their correctness based on the principles of fluid mechanics.

### Step-by-Step Solution:

1. **Evaluate Statement 1**: "Two points in the same horizontal plane cannot have the same pressure."
- This statement is **incorrect**. According to Pascal's law, in a static fluid, the pressure at any two points in the same horizontal plane is the same, provided they are at the same depth. The pressure at a point in a fluid is given by the formula \( P = \rho g h \), where \( h \) is the height of the fluid above that point. Since both points are at the same height, their pressures will be equal.

2. **Evaluate Statement 2**: "Two points at different levels may have the same pressure."
- This statement is **correct**. If a container with fluid is accelerated, the fluid surface will tilt, causing points at different vertical heights to have the same pressure. This can occur due to the dynamic effects of acceleration, which can equalize pressure at different heights.

3. **Evaluate Statement 3**: "Two points at different levels cannot have the same pressure."
- This statement is **incorrect**. As discussed in the evaluation of Statement 2, it is possible for two points at different heights to have the same pressure under certain conditions, such as when the fluid is subjected to acceleration.

4. **Evaluate Statement 4**: "Two points in the same vertical line always have different pressure."
- This statement is **incorrect**. While it is generally true that pressure increases with depth in a static fluid, there are scenarios (like in a flowing fluid with varying cross-sectional areas) where two points in the same vertical line can have the same pressure. According to Bernoulli's principle, if the velocity of the fluid changes, the pressure can also change, but not necessarily in a way that maintains a difference.

### Conclusion:
The only correct statement among the four is **Statement 2**: "Two points at different levels may have the same pressure."