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 oscillation

Explanation

To solve the problem of what happens to a steel ball floating in mercury when water is added to the trough, we can analyze the situation step by step.

### Step 1: Understand the Initial Setup
Initially, we have a steel ball floating in mercury. The steel ball is in equilibrium due to the buoyant force exerted by the mercury, which is equal to the weight of the steel ball.

**Hint:** Consider the concepts of buoyancy and equilibrium forces acting on the steel ball.

### Step 2: Introduce Water into the Trough
When we fill the empty part of the trough with water, we create a layered system where water is on top and mercury is below. The steel ball remains in the mercury but is now also affected by the water above it.

**Hint:** Think about how adding water changes the forces acting on the steel ball.

### Step 3: Analyze the Density of the Fluids
The density of water is less than that of mercury. This means that the water will exert a different buoyant force compared to the mercury. The steel ball will now experience buoyant forces from both the mercury and the water.

**Hint:** Recall that buoyant force is directly related to the density of the fluid and the volume of fluid displaced.

### Step 4: Calculate the Forces Acting on the Steel Ball
Let:
- \( F_1 \) be the buoyant force from the mercury.
- \( F_2 \) be the buoyant force from the water.

The total buoyant force acting on the steel ball is now \( F_{total} = F_1 + F_2 \). Since the steel ball is denser than both fluids, the addition of water increases the total buoyant force acting on the ball.

**Hint:** Consider how the buoyant force changes with the addition of water.

### Step 5: Determine the Movement of the Steel Ball
Since the total buoyant force \( F_{total} \) is now greater than the weight of the steel ball, it will cause the steel ball to rise. Therefore, the steel ball will move upwards in the trough.

**Hint:** Think about the balance of forces and how an increase in buoyant force affects the position of the steel ball.

### Conclusion
The steel ball will rise when water is added to the trough because the combined buoyant forces from both the mercury and the water exceed the weight of the steel ball.

**Final Answer:** The steel ball will move up.