In which of the following cases , the observer is in intertial frame?

Options

A. A child revolving in a merry-go-round
B. A driver in a car moving with a constant velocity
C. A pilot is an aircraft which is taking off
D. a passenger in a train which is showing down to stop

Answer

To determine in which of the following cases the observer is in an inertial frame, we need to understand what an inertial frame is. An inertial frame is one in which an observer is either at rest or moving at a constant velocity, meaning there are no net forces acting on the observer, and thus the acceleration is zero.

### Step-by-Step Solution:

1. **Understanding Inertial Frame**:
- An inertial frame is defined as a frame of reference in which a body remains at rest or moves at a constant velocity unless acted upon by a net external force. In such frames, Newton's first law holds true.

2. **Analyzing Each Case**:
- **Case 1: A child revolving in a merry-go-round**:
- In this case, the child is undergoing circular motion. The direction of the child's velocity is continuously changing, which means there is centripetal acceleration acting on the child. Therefore, this is **not** an inertial frame.

- **Case 2: A driver in a car moving with a constant velocity**:
- Here, the driver is moving at a constant velocity. There are no changes in speed or direction, which means the acceleration is zero. Thus, this is an inertial frame.

- **Case 3: A pilot in an aircraft which is taking off**:
- During takeoff, the aircraft is accelerating upwards. This means there is a net force acting on the pilot, resulting in non-zero acceleration. Therefore, this is **not** an inertial frame.

- **Case 4: A passenger in a train which is slowing down to stop**:
- In this scenario, the train is decelerating, which means the velocity is changing and there is a net force acting on the passenger. Hence, this is also **not** an inertial frame.

3. **Conclusion**:
- Based on the analysis, the only case where the observer is in an inertial frame is **Case 2: A driver in a car moving with a constant velocity**.

### Final Answer:
The observer is in an inertial frame in the case of **a driver in a car moving with a constant velocity**.