Question:
A cork of density 0.5 g/cm³ floats on a calm swimming pool. The fraction of the cork's volume which is underwater is:
a) 0%
b) 25%
c) 10%
d) 50%

Answer:
To determine the fraction of the cork's volume that is underwater, we need to analyze the buoyant force acting on the cork.

Buoyant Force:
The buoyant force is the upward force exerted on an object submerged in a fluid. It is given by the formula:

Buoyant force = weight of the fluid displaced

Archimedes' Principle:
According to Archimedes' principle, an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

Analysis:
In this case, the cork is floating on a calm swimming pool, which means the buoyant force acting on the cork is equal to its weight. We know that the density of the cork is 0.5 g/cm³.

To determine the fraction of the cork's volume underwater, we need to compare the densities of the cork and the fluid (water). If the density of the cork is less than the density of water, it will float.

Calculation:
The density of water is approximately 1 g/cm³. Since the density of the cork (0.5 g/cm³) is less than the density of water, it will float.

When an object floats, the buoyant force is equal to its weight. This means that the weight of the cork is equal to the weight of the fluid displaced by the cork.

Since the cork is floating, it displaces an amount of water equal to its own weight. Therefore, the fraction of the cork's volume underwater is equal to the ratio of the cork's weight to the weight of the fluid displaced.

The fraction of the cork's volume underwater can be calculated using the formula:

Fraction underwater = Weight of cork / Weight of fluid displaced

Since the weight of the cork is equal to the weight of the fluid displaced, the fraction underwater is equal to 1, or 100%.

Conclusion:
Therefore, the correct answer is option d) 50%.