If the system is not in free fall, which of the following, statements are true about hydrostatic pressure?

Options

A. In a liquid, points at different depths can never be at the same pressure.
B. In a liquid, points at different depths may be at the same pressure.
C. In different liquids, points at different depths can be at the same pressure.
D. In different liquids, points at the same depth can never be at same pressure.

Explanation

To determine which statements about hydrostatic pressure are true when the system is not in free fall, we can analyze each statement based on the principles of fluid mechanics.

### Step-by-Step Solution:

1. **Understanding Hydrostatic Pressure**:
Hydrostatic pressure in a fluid at a given depth is given by the formula:
\[ P = \rho g h \]
where \(P\) is the pressure, \(\rho\) is the density of the fluid, \(g\) is the acceleration due to gravity, and \(h\) is the depth of the fluid.

2. **Analyzing Statement 1**:
The first statement claims that "in a liquid, points at different depths can never be at the same pressure."
- Since pressure increases with depth (as \(h\) increases), this statement is **true**. Points at different depths will have different pressures.

3. **Analyzing Statement 2**:
The second statement claims that "in a liquid, points at different depths may be at the same pressure."
- This contradicts the first statement. Since we established that pressure varies with depth, this statement is **false**.

4. **Analyzing Statement 3**:
The third statement claims that "in different liquids, points at different depths can be at the same pressure."
- This can be true if the product of density and height is equal for the two different liquids. For example, if \(\rho_1 h_1 = \rho_2 h_2\), then the pressures can be equal. Thus, this statement is **true**.

5. **Analyzing Statement 4**:
The fourth statement claims that "in different liquids, points at the same depth can never be at the same pressure."
- If we consider two different liquids at the same depth, the pressures will depend on their densities. Since the densities are different, the pressures will also be different. Therefore, this statement is **true**.

### Conclusion:
Based on the analysis, the true statements about hydrostatic pressure when the system is not in free fall are:
- Statement 1: True
- Statement 2: False
- Statement 3: True
- Statement 4: True

Thus, statements 1, 3, and 4 are true.