Water Level floating ice physics

[Chewy0087]

Homework Statement

another conceptual problem I'm having here, goes like this;

A piece of ice floats in a glass filled with water. The ice contains a small stone, so that when the ice has melted the stone will sink to the bottom of the glass. What will happen to the water level of the glass as firstly, the ice melts, and secondly, the stone falls to the bottom of the glass.

A)Rise then stay the same
B)Rise then fall
C)Fall then remain the same
D)Remain the same, then fall.

The Attempt at a Solution

well my thought process was like so, ice is more dense than water, and because of p = mass / volume, and the mass is the same, it's volume would be greater when it melts causing the water level to rise, however I'm confused as to the effect of it all as I'm not sure if/how to consider buoyancy...

the answer is D) and i simply can't see why, sureley when the stone is in the ice, the ice displaces the stones weight in the water, so why would the water level fall when the stone falls in?

any help would be appreciated ...

 

[willem2]

Ice is less dense than water (if floats!) While it is floating, it will displace a volume of water equal to its own weight. After it melts it will still displace a volume equal to its own weight.
(and now equal to its volume as well)

The stone displaces the stones weight in water while it is in the ice. After the stone falls in, it will only displace a volume equal to its own volume, which is less, because the stone is more dense than water.

 

[Chewy0087]

great explanation, thank you