A piece of ice is floating in a jar containing water. When the ice melts, then the level of water

Options

A. rises
B. falls
C. remains unchaged
D. rises or falls depending upon the mass of ice

Answer

To solve the problem of whether the water level in a jar rises, falls, or remains unchanged when a piece of ice floating in it melts, we can use the principles of buoyancy and Archimedes' principle.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- We have a jar filled with water and a piece of ice floating on the surface. The ice is partially submerged due to buoyancy.

**Hint**: Visualize the setup: a jar with water and ice floating on top.

2. **Applying Archimedes' Principle**:
- According to Archimedes' principle, the weight of the water displaced by the ice is equal to the buoyant force acting on the ice. This buoyant force is what keeps the ice afloat.

**Hint**: Recall that the buoyant force is equal to the weight of the fluid displaced.

3. **Weight of the Ice**:
- The weight of the ice can be expressed as the mass of the ice multiplied by the acceleration due to gravity (W_ice = m_ice * g).

**Hint**: Remember that weight is a force and is calculated as mass times gravity.

4. **Volume of Water Displaced**:
- The volume of water displaced by the ice can be calculated using the formula: Volume = Mass / Density. The density of water is approximately ρ (rho).

**Hint**: Use the formula for volume displacement: V = m / ρ.

5. **Calculating Water Level Change**:
- When the ice melts, it turns into water. The volume of water produced by the melting ice is equal to the volume of water that was displaced when the ice was floating.

**Hint**: Think about the conservation of volume: the melted ice occupies the same volume as the water it displaced.

6. **Conclusion**:
- Since the volume of water produced by the melting ice is equal to the volume of water displaced while the ice was floating, the overall water level in the jar remains unchanged.

**Hint**: Compare the volume of displaced water with the volume of melted ice to see that they are equal.

### Final Answer:
The level of water remains unchanged when the piece of ice melts.