The pressure in a liquid at two points in the same horizontal plane are equal. Consider an elevator accelerating upward and a car accelerating on a horizontal road. The above statement is correct in

Options

A. the car only
B. the elevator only
C. both of them
D. neither of them

Answer

To solve the problem, we need to analyze the pressure in a liquid at two points in the same horizontal plane under two different scenarios: an elevator accelerating upwards and a car accelerating horizontally.

### Step-by-Step Solution:

1. **Understanding Pressure in a Fluid**:
- The pressure at a certain depth in a fluid is given by the equation:
\[ P = P_0 + \rho g h \]
where \( P_0 \) is the pressure at the surface, \( \rho \) is the density of the fluid, \( g \) is the acceleration due to gravity, and \( h \) is the depth from the surface.

2. **Analyzing the Elevator Scenario**:
- When the elevator accelerates upwards with acceleration \( a \), the effective acceleration acting on the fluid becomes \( g + a \).
- However, since we are looking at points in the same horizontal plane, the height \( h \) remains constant for both points.
- Therefore, the pressure at two points in the same horizontal plane inside the elevator can be expressed as:
\[ P_A = P_0 + \rho (g + a) h \]
\[ P_{A'} = P_0 + \rho (g + a) h \]
- Since both points are at the same height \( h \), we conclude that \( P_A = P_{A'} \). Thus, the pressure is equal at both points.

3. **Analyzing the Car Scenario**:
- When the car accelerates horizontally, the fluid inside the car will not remain level due to the horizontal acceleration.
- The fluid will tilt, creating a difference in height between two points in the same horizontal plane.
- Let’s denote the heights at two points as \( h_1 \) and \( h_2 \). Due to the tilt, \( h_1 \) will not equal \( h_2 \).
- The pressures at these two points can be expressed as:
\[ P_A = P_0 + \rho g h_1 \]
\[ P_{A'} = P_0 + \rho g h_2 \]
- Since \( h_1 \neq h_2 \), it follows that \( P_A \neq P_{A'} \). Therefore, the pressure is not equal at these two points.

4. **Conclusion**:
- The statement that the pressure in a liquid at two points in the same horizontal plane are equal is only correct in the case of the elevator accelerating upwards. In the case of the car accelerating horizontally, the pressures are not equal due to the change in fluid level.

### Final Answer:
The above statement is correct only in the case of the elevator accelerating upwards.