A steel ball is floating in a trough of mercuty. If we fill the empty part of the trough with water, what will happen to the steel ball ?

Options

A. it will continue in its position
B. it will move up
C. it will move down
D. it will execute vertical oscillations

Answer

To solve the problem of what happens to a steel ball floating in mercury when the empty part of the trough is filled with water, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- Initially, the steel ball is floating in mercury. The buoyant force acting on the ball is equal to the weight of the ball. Since the density of mercury is much higher than that of water, the steel ball floats at a certain level in the mercury.

2. **Adding Water to the Trough**:
- When we start filling the empty part of the trough with water, we need to consider the density of water compared to mercury. Water has a lower density than mercury.

3. **Forces Acting on the Steel Ball**:
- The steel ball experiences two upward buoyant forces:
- **F1**: The buoyant force due to the mercury.
- **F2**: The buoyant force due to the water once it is added.
- As we add water, the water will exert an upward buoyant force on the ball.

4. **Effect of Water on the Buoyant Force**:
- The addition of water increases the total buoyant force acting on the steel ball because now both the mercury and the water are exerting upward forces. The buoyant force from the water is less than that from mercury, but it contributes to the total buoyant force.

5. **Conclusion**:
- Since the steel ball is already floating in mercury and the addition of water increases the overall buoyant force acting on the ball, the steel ball will rise higher in the mercury as the water is added.

### Final Answer:
The steel ball will move up when the empty part of the trough is filled with water.