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 on a horizontal road.

### Step-by-Step Solution:

1. **Understanding Pressure in a Liquid**:
The pressure at a point in a liquid is given by the formula:
\[ P = P_0 + \rho g h \]
where \( P_0 \) is the atmospheric pressure, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the depth of the liquid column above the point.

2. **Case 1: Elevator Accelerating Upwards**:
- When the elevator accelerates upwards, the liquid inside the elevator experiences an effective increase in pressure due to the upward acceleration.
- However, the surface of the liquid remains horizontal because the entire system (elevator and liquid) is accelerating uniformly.
- Therefore, at any two points in the same horizontal plane within the liquid, the depth \( h \) remains the same, and thus the pressure at these two points will be equal:
\[ P_A = P_0 + \rho g h_A \quad \text{and} \quad P_B = P_0 + \rho g h_B \]
Since \( h_A = h_B \), it follows that \( P_A = P_B \).

3. **Case 2: Car Accelerating on a Horizontal Road**:
- In this scenario, when the car accelerates horizontally, the liquid inside the car will not remain level.
- Due to the inertia of the liquid, it will tilt towards the back of the car, creating a sloped surface.
- As a result, the depth of the liquid at one end of the container will be different from the depth at the other end. Let’s denote these depths as \( h_A \) and \( h_B \).
- Therefore, the pressure at these two points will be different:
\[ P_A = P_0 + \rho g h_A \quad \text{and} \quad P_B = P_0 + \rho g h_B \]
Since \( h_A \neq h_B \), it follows that \( P_A \neq P_B \).

4. **Conclusion**:
- From the analysis, we conclude that the pressure in a liquid at two points in the same horizontal plane is equal when the elevator is accelerating upwards, but not equal when the car is accelerating on a horizontal road.
- Therefore, the correct statement is that the pressure in the liquid at two points in the same horizontal plane is equal in the case of the elevator.

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

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