Question

A piece of ice floating in a glass of water melts, but the level of water in glass does not change. Give reason.
A. Ice contracts on melting.
B. Ice expands on melting.
C. Ice has the same density as that of water.
D. Ice has density less than that of water.

Answer 1

Hint: Use the principle of Archimedes. According to which a body floating in a liquid displaces the weight of liquid equal to its own weight.

Complete step-by-step solution:
It is true because in both the cases weight of water displaced and equal weight of ice and weight of ice before and after melting is the same.
This follows Archimedes principle, according to which a body floating in a liquid displaces weight of liquid equal to its own weight.
Ice displaces exactly its equivalent mass of water when it floats, the ice melts there is no change in the amount of water in the vessel so the water level does not rise
The level does not change because the ice is nearly at neutral buoyancy or barely floating to begin with, and it is colder.
A tiny amount of the ice often protrudes above the water, so it does not have exactly neutral buoyancy, but it is close.
One need only observe that Icebergs have exposed surfaces. Even in freshwater that rises above the water surface, something happens in a glass. Since part is above water, the ice must be displacing a greater mass of water. So density change must play a part.
As the ice melts it warms but does not expand, since warming ice above freezing causes contraction not expansion (water reaches its maximum density at ${4^\circ}C$ well above freezing).
The warming ice cools the surrounding water thus decreasing its volume. The net result is that floating ice does not raise water levels when it melts; they stay the same.

Therefore options A and D are the correct answers.

Note: Students should remember the freezing and boiling point of water. The freezing point of water or melting point of ice is $273K$ or ${0^\circ}C$. Whereas the boiling point of water is $373K$ or ${100^\circ}C$. Not every material has a graph like water. Only in water its density increases, as it changes state from solid to liquid, for a little while and then decreases.