Question

A piece of ice is floating in a glass vessel filled with water. Then prove that level of water in the vessel remains unchanged after melting of ice.

Answer 1

To Prove :-

We have to prove that level of water in the vessel remains unchanged after melting of ice.

Solution:-

Let m be the mass of ice piece floating in water.

In equilibrium condition weight of ice piece = upthrust

i.e  mg = $V_{in}$$p_{w}g$

or

$V_{in} = \frac{m}{p_{w} }$............(1)

Where $V_{in}$ is the volume of ice piece immersed in water and $p_{w}$ density of water.

When ice melt , Let V be the volume of water formed by mass of ice, then

V = $\frac{m}{p_{w} }$...............(2)

using equation (1) and (2) then

$V_{in} = V$

Hence, the level remains unchanged