A ball is located in a semicircular trough. The ball is moved slightly to one side and returns to its original locatiun. The ball Is said to be in

Options

A. neutral equilibrium
B. unstable equilibrium
C. stable equilibrium
D. all of the above.

Explanation

To solve the problem, we need to analyze the situation of a ball placed in a semicircular trough and determine the type of equilibrium it exhibits when slightly displaced.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a semicircular trough and a ball resting at the bottom of this trough. The ball is in a stable position due to the shape of the trough.

2. **Displacing the Ball**:
- When the ball is moved slightly to one side, it is displaced from its original position.

3. **Forces Acting on the Ball**:
- The gravitational force (mg) acts downward on the ball. When the ball is displaced, there are components of this gravitational force that come into play.
- The component of the gravitational force acting along the direction of the trough will pull the ball back towards the center.

4. **Returning to Original Position**:
- As the ball is displaced, the restoring force (due to the component of mg acting along the trough) will cause the ball to roll back to its original position.
- If the ball overshoots the center, it will continue to move to the opposite side but will eventually return to the center again.

5. **Identifying the Type of Equilibrium**:
- Since the ball returns to its original position after being displaced, it indicates that the equilibrium is stable.
- In stable equilibrium, any small displacement results in a restoring force that brings the object back to its original position.

6. **Conclusion**:
- Therefore, the ball is said to be in **stable equilibrium**.

### Final Answer:
The ball is in **stable equilibrium**.