A block of ice with a lead shot embedded in it is floating on water contained in a vessel. The temperature of the system is maintained at `0^@C` as the ice melts. When the ice melts completely the level of water in the vessel rises.

Explanation

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

### Step 1: Understand the System
We have a block of ice floating on water in a vessel. The ice has a lead shot embedded in it, and the entire system is maintained at a temperature of \(0^\circ C\).

### Step 2: Consider the Principle of Buoyancy
According to Archimedes' principle, the weight of the water displaced by the floating ice is equal to the weight of the ice plus the weight of the lead shot.

### Step 3: Calculate the Weight of the Ice and Lead Shot
Let:
- \(m_i\) = mass of the ice
- \(m_l\) = mass of the lead shot
- \(V_i\) = volume of the ice
- \(V_w\) = volume of water displaced

The weight of the ice and lead shot combined is given by:
\[ W = (m_i + m_l)g \]
where \(g\) is the acceleration due to gravity.

### Step 4: Calculate the Volume of Water Displaced
The volume of water displaced by the ice can be calculated using the density of water (\(\rho_w\)):
\[ V_w = \frac{W}{\rho_w g} = \frac{(m_i + m_l)g}{\rho_w g} = \frac{(m_i + m_l)}{\rho_w} \]

### Step 5: Analyze the Melting of Ice
As the ice melts, it turns into water. The volume of water produced from the melted ice can be calculated using the density of ice (\(\rho_i\)):
\[ V_{water\ from\ ice} = \frac{m_i}{\rho_i} \]

### Step 6: Determine the Final Water Level
When the ice melts completely, the volume of water from the melted ice plus the lead shot will contribute to the water level in the vessel. The total volume of water after melting will be:
\[ V_{total} = V_{water\ from\ ice} + V_w \]

### Step 7: Conclusion
Since the ice was already floating, the water level in the vessel will rise when the ice melts completely, as the volume of water produced from the melted ice will be equal to the volume of water displaced by the ice and the lead shot.

### Final Answer
The level of water in the vessel rises when the ice melts completely.

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