Question

A piece of ice is floating in a glass vessel filled with water. How will the level of water in the vessel change when the ice melts?

Answer 1

Hint:-Here, we will apply or the Archimedes principle to calculate the level of water in the vessel.
Archimedes principle states that that when a body is fully or partially submerged in a fluid then a upward buoyant force is exerted on the body which is equal to the weight of fluid displaced by the body.Mathematically, it is written as,
\[W = {F_B}\]

Complete step-by-step solution:-
Given that:
A piece of ice is floating in a glass vessel.
Let m is the mass of the ice piece floating in the water.
First of all, the law of floatation will be applied till the situation where the ice is floating in a vessel.
The law of floatation states that the weight of the fluid displaced by the body is equal to the weight of the body. Mathematically, it is written as,
 \[{\text{W = }}{{\text{W}}_{{\text{displace}}}}\] …… (2)
Now compare the equation (1) and (2),
\[{F_B} = {{\text{W}}_{{\text{displace}}}}\] …… (3)
Now calculate the values for equation (3)
Here, \[{\text{V}}\]is the volume of the water which is formed by melting of ice.
 \[{{\text{V}}_{{\text{displaced}}}}\] is the volume of water which is displaced by the ice piece.
Hence it is proved that the level of water in the vessel will not change when the ice melts.

Note:- the amount of water displaced by the floating ice is equal to the amount of water melt by the ice piece. Therefore, the level of water in the vessel will be the same after the melting of the ice piece.