If ice cubes floating on water in an open vessel are allowed to melt completely, what will happen to the water level in the vessel once all the ice has melted?

Introduction / Context:
This question explores an interesting application of the principle of flotation and density. Ice is less dense than liquid water, which is why it floats. Many learners wonder whether the water level in a glass or vessel changes when floating ice melts. Understanding this situation helps to clarify Archimedes principle and the idea of displaced volume, and it also gives an intuitive explanation of why floating sea ice melting does not directly raise sea levels.

Given Data / Assumptions:

• Ice cubes are floating on the surface of water in a vessel.
• The ice is completely above and below the water line as in a normal floating situation.
• The system is open to the atmosphere and no water is added or removed.
• The ice is allowed to melt completely without any evaporation losses being considered.

Concept / Approach:
When a body floats, it displaces a volume of liquid whose weight equals the weight of the body, as stated by Archimedes principle. Ice has a lower density than liquid water, so a portion of its volume remains above the surface, but the submerged part displaces water. The weight of this displaced water is equal to the weight of the ice. When the ice melts, it turns into liquid water of the same mass. This melted water exactly occupies the volume that was previously displaced, because mass is conserved and the density is now that of liquid water. As a result, the overall water level in the vessel remains unchanged after melting.

Step-by-Step Solution:
Step 1: Recognise that floating ice displaces a volume of water whose weight equals the weight of the ice.Step 2: Let the mass of a piece of ice be m; its weight is m * g, where g is acceleration due to gravity.Step 3: The displaced water has mass m as well, because its weight m * g equals the weight of the ice.Step 4: When the ice melts, it becomes water of mass m and density equal to that of the surrounding water.Step 5: This melted water occupies exactly the same volume as the water that was displaced earlier, so the water level remains the same.

Verification / Alternative check:
You can perform a simple experiment by placing a few ice cubes in a glass of water, marking the initial water level on the glass, and then waiting for the ice to melt at room temperature. You will observe that the final water level matches the initial mark closely if evaporation is negligible. This experimental check confirms the theoretical prediction. The reasoning also explains why melting of floating sea ice, such as icebergs, does not directly raise ocean levels, although other forms of ice melt, like land based glaciers, do have an effect.

Why Other Options Are Wrong:
If the water level increased, as in option A, it would imply that the melted water occupies more volume than the water originally displaced by the ice, which contradicts the equality of weights and densities. Option C, which suggests the level first rises and then falls, has no physical basis in this simple system. Option D, stating that the water level decreases, would imply that the melted water occupies less volume than was originally displaced, which is also incorrect. Only option B, that the water level does not change, is consistent with Archimedes principle and practical observation.

Common Pitfalls:
Many learners mistakenly think that melting ice always raises water levels because they focus on the extra water being added without considering displacement. Others wrongly apply intuition from adding ice to an empty container instead of to water. The key idea is that a floating object already causes a displacement equal to its weight. When it melts and becomes part of the liquid, the volume it occupies is exactly the same as the volume of water it previously displaced. Keeping this mass and displacement reasoning in mind helps avoid confusion in similar buoyancy problems.

Final Answer:
The water level does not change