A small lead shot is embedded in a big lump of ice floating in a jar of water. The level of water in the jar is noted. When all the ice melts down, the level of water in the jar would

Options

A. be raised
B. go down
C. remain unchanged
D. None of these

Explanation

To solve the problem, we need to analyze the situation step by step:

### Step 1: Understand the Initial Situation
- We have a lump of ice floating in water, with a lead shot embedded in it. The ice is floating, which means it displaces a volume of water equal to the weight of the ice plus the weight of the lead shot.

### Step 2: Apply the Principle of Buoyancy
- According to Archimedes' principle, the buoyant force acting on the ice is equal to the weight of the water displaced by the ice.
- Let \( V \) be the total volume of the ice, \( \rho_{ice} \) be the density of ice, and \( \rho_{water} \) be the density of water. The weight of the ice plus the lead shot can be expressed as:
\[ W = V \cdot \rho_{ice} \cdot g + m_{lead} \cdot g \]
where \( m_{lead} \) is the mass of the lead shot.

### Step 3: Calculate the Volume of Water Displaced
- The volume of water displaced by the ice can be calculated using the buoyant force:
\[ F_b = V_{displaced} \cdot \rho_{water} \cdot g \]
- Setting the weight equal to the buoyant force gives:
\[ V \cdot \rho_{ice} \cdot g + m_{lead} \cdot g = V_{displaced} \cdot \rho_{water} \cdot g \]

### Step 4: Determine the Fraction of Ice Submerged
- The fraction of the ice submerged can be expressed as:
\[ f = \frac{m_{lead} + V \cdot \rho_{ice}}{V_{displaced} \cdot \rho_{water}} \]
- Since the ice is floating, the volume of water displaced is equal to the weight of the ice and the lead shot.

### Step 5: Analyze the Melting of Ice
- When the ice melts, it will turn into water. The volume of water produced from the melting ice can be calculated as:
\[ V_{water\_from\_ice} = V \cdot \frac{\rho_{ice}}{\rho_{water}} \]
- This volume of water will be less than the original volume of water displaced by the ice.

### Step 6: Conclusion on Water Level Change
- Since the volume of water produced from the melted ice is less than the volume of water that was displaced while the ice was floating, the overall water level in the jar will decrease when the ice melts.

### Final Answer
- Therefore, the level of water in the jar would **decrease** when all the ice melts down.

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