Question

Question #f9e45

Answer 1

No change.

Explanation:

First of all let us discuss the missing information in the question. The density of water depends on its temperature as shown in the figure below.

In the question we are required to find out change of volume of water, ice and cork combine around `0^@C` when ice has melted.
We know that `"Density"="Mass" /"Volume"`.

Therefore, we make an assumption that the temperature does not change and remains at `0^@C` after ice has melted.
Composition of masses of ice and embedded cork piece is not given so a general assumption has been made as below.

Density in (`10^3kgm^-3`) of water at `0^@C=0.99985approx1,` ice `=0.917` and of cork `approx0.24`.

Archimedes' Principle states that for any object which is floating in a fluid, the weight of the fluid displaced by the object is equal to its own weight.

When ice block with cork embedded in it floats in water, the upthrust created on the ice block is equal to the weight of the water displaced by it. The volume of water displaced is equal to the volume of the ice block submerged in water. A small part of the ice block remain out of water.

When ice melts, its volume shrinks and it becomes water. However, its weight remains the same and is exactly equal to the weight of displaced water when the ice block existed. As the melted ice occupies volume equal to volume of water it initially displaced. Therefore, melting of ice does not change the water level.

In case of cork, it displaces water equal to its weight whose volume is equal to the volume of cork submerged in the water.
Volume of ice block sticking outside the water will depend on the mass composition of the block.

In the given case it can be seen that ice+cork block being lighter than ice only block of same volume will submerge less in water than if it were ice only. This is due to fact that ice being denser than cork will make the block sink more if it were cork only and cork being lighter than ice will make less part of ice block sink than ice only block.

In given case when ice melts volume of water level will remain same as shown below.

Suppose there are `x` cc of ice and `y` cc of cork in the block. Using CGS system of units.

Weight of floating block `=x xx0.917+yxx0.24=0.917x+0.24y " g"`
Water displaced`=0.917x+0.24y " g"`
Change in volume`=0.917x+0.24y" cc"` .....(1)

After melting ice will occupy volume`=0.917x" cc"`
Weight and volume of cork do not change.
Therefore, weight of water displaced by floating cork`=0.24y` g Volume of water displaced `=0.24y" cc"`
Total change in volume `=0.917x+0.24y" cc"` .....(2)