Question

A cube of ice of specific gravity $0.90$ floats in a cup of water. Several hours later, the ice cube has completely melted into the glass. How does the water level after melting compare to the initial water level?
A) The water level is unchanged after melting.
B) The water level is 10% higher after melting.
C) The water level is 90% higher after melting.
D) The water level is 10% lower after melting.

Answer 1

Hint: The answer is simply based on Archimedes’ principle which states that when a body is fully or partially submerged in a liquid then the upward buoyant force exerted on a body is equal to the weight of the fluid that the body displaces.

Complete step by step answer:
Step1:
Principle of floatation: - A floating object displaces a fluid having a weight equal to the weight of the object. An object sinks if its weight is greater than that of the upthrust acting on it. An object floats if its weight is equal or less than the upthrust.
When an object floats in a fluid, the upthrust acting on it is equal to the weight of the object. In the case of a floating object, the object may be partially immersed. The upthrust is always equal to the weight of the fluid displaced by the object. This is the principle of floatation.
Step2:
Here, the body is ice which is floating in the cup of water. So according to the Archimedes’ principle, the volume of the water displaced by ice is equal to the total weight of the ice. When the ice melts and gets converted into the water, then the volume of the melted ice equals the initial volume of ice inside the water. Hence, the level of water does not change.

$\therefore$The water level is unchanged after the melting of the ice cube. Hence, option (A) is correct.

Additional information:
1. Here are some of the applications/examples of Archimedes’ principle.
(i) Floating of ships.
(ii) Ice cubes in the glass of water.
(iii) Feeling upthrust in the bathtub.
2. The specific gravity of an object is the density of that object divided by the density of the water.
Specific gravity =$\dfrac{{density\left( {object} \right)}}{{density\left( {water} \right)}}$
Or we can write it in mathematical language as, $\dfrac{{{\rho _{object}}}}{{{\rho _{{H_2}O}}}}$ where $\rho $ denoted density.
If a substance has a specific gravity less than that of fluid then it will float on that fluid.
Examples/Application of specific gravity:
(a) The density of liquid mercury has a density of 13.6 kg, therefore it floats.
(b) Helium-filled balloons will rise in the air.
(c) Oil will form a slick on water.
(d) Lead will float on mercury
3. Fact: Water at ${4^0}C$ has the maximum density and is taken to have the value $999.974$ kg${m^{ - 3}}$. It is therefore a relative quantity with no units.


Note:
There is one more way which is a self example. We can see that during the winter season there are so many icebergs and ice stones freeze near the water bodies. But during the summer season they melt and still, there are no flood-like situations. This implies that no increase in the volume of water happens. It remains the same.