Question

A piece of ice is floating on water in a container. What will happen to the surface of water when whole ice piece melts :
1. will go up
2. will not change
3. will go down
4. none of these

Answer 1

Correct Answer - Option 2 : will not change

The correct answer is option 2) i.e. will not change.

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 (F_B) is given by,

F_B = ρ_fluid × g × V_object

​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 = ρ_water × V_{dispalced 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 = V_dispalced 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.