A cork floats on water while an iron nail of the same mass sinks. This is best explained by the fact that:

Correct Option

The correct option is

The density of the cork is less than that of water, whereas the density of the nail is greater.

Explanation

The phenomenon of flotation is governed by the principle of buoyancy and relative density. Whether an object floats or sinks in a fluid depends on the relationship between the density of the object and the density of the fluid. According to Archimedes' principle, an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

Statement-wise Analysis

• The volume of the cork is less than that of the nail.: Incorrect. While it is true that for the same mass, the cork has a larger volume than the iron nail (because cork is less dense), the volume difference itself is a consequence of density. The primary physical condition determining flotation is the comparison of densities, not just volume in isolation.
• The density of the cork is less than that of water, whereas the density of the nail is greater.: Correct. An object floats if its density is less than that of the fluid. The density of cork is significantly lower than that of water, meaning the upthrust (buoyant force) exerted by the water is sufficient to balance the weight of the cork before it is fully submerged. Conversely, the density of iron is greater than that of water, resulting in a weight that exceeds the maximum buoyant force, causing the nail to sink.
• The gravitational force acting on the cork is less than that on the nail.: Incorrect. The gravitational force (weight) acting on an object is given by the formula \( W = mg \). Since the question states that the cork and the nail have the same mass, the gravitational force acting on both is identical. Therefore, a difference in gravitational force cannot explain why one floats and the other sinks.
• The surface tension of water supports the cork but not the nail.: Incorrect. Surface tension is a property of the liquid surface that allows it to resist an external force, typically supporting very light or small objects (like a needle or an insect) without them breaking the surface. It is not the dominant force responsible for the flotation of macroscopic objects like a cork; buoyancy is the governing factor.

Key Takeaway: An object will float in a fluid if its density is less than the density of the fluid. If the object's density is greater than that of the fluid, it will sink.