Question

An ice cube contains a large air bubble. The cube is floating on the surface of water contained on a trough. What will happen to the water level, when the cube melts?

• A. It will remain unchanged
• B. It will fall
• C. Increases with temperature
• D. Decreases with temperature

Answer 1

The correct option is A

It will remain unchanged

Let the density of ice be ${\rho }_i$

Let the volume of the cube be V and that of the bubble be V'.

Mass of ice melted = (V - V')${\rho }_i$= mass of water melted.

∴ Volume of water melted =$(V-V^{\prime })\frac{{\rho }_i}{{\rho }_{\omega }}$

Now when the cube was floating,

Mass of water displaced = mass of ice cube

= (V - V')${\rho }_i$

$\therefore$ Volume of water displaced =$(V-V^{\prime })\frac{{\rho }_i}{{\rho }_{\omega }}$

We can see that the volume of water displaced is equal to the volume of water produced due to melting. Therefore the level will remain unchanged.