A block of ice in which a piece of stone is embedded is floating on water contained in a beaker. When all the ice melts the level of water in the beaker

Options

A. rises
B. falls
C. remains unchanged
D. None of the above

Explanation

To solve the problem of a block of ice with a stone embedded in it floating in water, we need to analyze the situation step by step.

### Step 1: Understand the Initial Condition
The block of ice is floating in water. According to Archimedes' principle, the weight of the water displaced by the ice is equal to the weight of the ice plus the weight of the stone embedded in it.

**Hint:** Remember that floating objects displace their weight in fluid.

### Step 2: Determine the Volume of Water Displaced
When the ice is floating, it displaces a volume of water equal to the weight of the entire system (ice + stone). The volume of water displaced can be calculated using the formula:
\[ V_{\text{displaced}} = \frac{W_{\text{total}}}{\rho_{\text{water}} g} \]
where \( W_{\text{total}} \) is the total weight of the ice and stone, \( \rho_{\text{water}} \) is the density of water, and \( g \) is the acceleration due to gravity.

**Hint:** Consider the relationship between weight and volume for floating objects.

### Step 3: Analyze the Melting of Ice
When the ice melts, it turns into water. The volume of water produced from the melting ice is equal to the volume of the ice itself. However, the stone does not change the water level since it is already submerged.

**Hint:** Remember that the volume of melted ice will occupy the same space as the ice did when it was floating.

### Step 4: Compare the Water Levels
Initially, the water level is determined by the volume of water displaced by the floating ice and stone. After the ice melts, the water level will be determined by the volume of water produced from the melted ice and the volume of the stone submerged.

Since the volume of water produced from the melted ice is equal to the volume of the ice that was previously displacing water, the total water level remains unchanged.

**Hint:** Think about how the melting of ice affects the total volume of water in the beaker.

### Step 5: Conclusion
After the ice melts, the water level in the beaker will remain the same. The stone does not affect the water level change since it was already submerged.

**Final Answer:** The level of water in the beaker will remain the same.

---