A ball is hung by a string from the ceiling of a car moving on a straight and smooth road. If the string is inclined towards the front side of the car making a small constant angle with the vertical, then the car is moving with

Options

A. Constant velocity
B. Constant acceleration
C. Constant retardation
D. Increasing acceleration

Explanation

To solve the problem, we need to analyze the situation of a ball hung from the ceiling of a car that is moving on a straight and smooth road. The ball is inclined towards the front side of the car, making a small angle with the vertical. We need to determine the motion of the car based on this information.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A ball is suspended from the ceiling of a car.
- The car is moving on a straight and smooth road.
- The string holding the ball is inclined towards the front of the car, indicating that there is a net force acting on the ball.

2. **Analyzing Forces on the Ball**:
- The ball experiences two main forces:
- The gravitational force acting downwards (weight of the ball).
- The tension in the string, which acts along the string and has a vertical and horizontal component.

3. **Identifying the Angle**:
- The inclination of the string towards the front of the car suggests that there is a horizontal component of force acting on the ball.
- This horizontal component is due to the acceleration of the car.

4. **Considering Different Cases**:
- **Case 1: Car at Rest**: If the car is at rest, the ball would hang vertically downwards, and the string would not be inclined.
- **Case 2: Car Moving with Constant Velocity**: If the car moves with a constant velocity, there is no net force acting on the ball, and it would also hang vertically.
- **Case 3: Car Accelerating**: If the car accelerates forward, the ball would experience a pseudo force acting backward, causing the string to incline towards the front of the car. However, this would not create a stable equilibrium with a small angle.
- **Case 4: Car Decelerating (Constant Retardation)**: If the car is decelerating, the pseudo force acting on the ball would be directed towards the front of the car, causing the string to incline towards the front, which matches our observation.

5. **Conclusion**:
- The only scenario where the string is inclined towards the front of the car is when the car is moving with constant retardation. This is because the pseudo force acting on the ball would be in the direction opposite to the car's motion, resulting in the inclination of the string towards the front.

### Final Answer:
The car is moving with **constant retardation**.