Select the correct option

Options

A. As we move down through a liquid at rest the pressure increases
B. As we move along horizontal through a liquid at rest the pressure remains unchanged
C. As we move along horizontal through a liquid subjected to a horizontal acceleration, the pressure increases in the direction of acceleration
D. The gauge pressure at a point inside a liquid depends on atmospheric pressure

Answer

To solve the question regarding the properties of pressure in liquids, we will analyze each of the provided options step by step.

### Step 1: Analyze Option 1
**Statement**: As we move down through a liquid at rest, the pressure increases.

**Explanation**:
- In a liquid at rest, the pressure at a certain depth is given by the formula:
\[ P = \rho g h \]
where \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the depth from the surface of the liquid.
- As we move deeper (downward), \( h \) increases, which leads to an increase in pressure.
- Therefore, this statement is **correct**.

### Step 2: Analyze Option 2
**Statement**: As we move along the horizontal through a liquid at rest, the pressure remains unchanged.

**Explanation**:
- For a liquid at rest, the pressure at the same horizontal level is constant.
- If we consider two points at the same depth (horizontal level), the pressure at both points will be the same:
\[ P_A = P_B = \rho g h \]
- Thus, this statement is also **correct**.

### Step 3: Analyze Option 3
**Statement**: As we move along horizontal through a liquid subjected to a horizontal acceleration, the pressure increases in the direction of acceleration.

**Explanation**:
- When a liquid is subjected to horizontal acceleration, a pseudo force acts on it in the opposite direction of the acceleration.
- This causes the liquid to rise on the side opposite to the direction of acceleration.
- Therefore, the pressure actually increases in the opposite direction of the acceleration, making this statement **incorrect**.

### Step 4: Analyze Option 4
**Statement**: The gauge pressure at a point inside a liquid depends on the atmospheric pressure.

**Explanation**:
- Gauge pressure is defined as the pressure relative to atmospheric pressure. It is calculated as:
\[ P_{\text{gauge}} = P_{\text{absolute}} - P_{\text{atmospheric}} \]
- However, gauge pressure itself is determined by the height of the liquid column above the point in question:
\[ P_{\text{gauge}} = \rho g h \]
- Hence, gauge pressure does not depend on atmospheric pressure; it only depends on the height of the liquid column. Thus, this statement is **incorrect**.

### Conclusion
The correct options are:
- **Option 1**: Correct
- **Option 2**: Correct
- **Option 3**: Incorrect
- **Option 4**: Incorrect

### Final Answer
The correct options are **Option 1 and Option 2**.

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