Question

A cup of water is filled to the brim, with an ice cube in it. The top of the ice cube sticks out of the surface. What happens when the ice melts?
1. the cup overflows
2. the water level remains the same
3. the water level decreases
4. none of the above

Answer 1

Correct Answer - Option 2 : the water level remains the same

The correct answer is option 2) i.e. the water level remains the same

CONCEPT:

• Archimedes' principle: A body at rest in a fluid is acted upon by a force pushing it upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.

​The buoyant force (FB) is given by,

FB = ρfluid × g × Vobject

​EXPLANATION:

The floating ice will displace some volume of the water.

From Archimedes' principle, FB = ρwater × g × Vice      ----(1)

Weight of the displaced fluid (water) = mg = ρwater × Vdispalced water × g      ----(2)

For an object to stay afloat, the forces acting on it must be balanced ⇒ (1) = (2)

ρwater × g × Vice = ρwater × Vwater × g 

⇒  Vice = Vdispalced water

Therefore, when the ice melts, there will be no change in the water level as the melted ice will occupy the same volume as that of displaced water.