Which of the following determines an object's ability to float in water?

• A. The object's color
• B. The object's mass alone
• C. The object's surface area alone
• D. The ratio of the object's density to the density of water $\frac{\rho }{{\rho }_{\mathrm{water}}}$

Answer: (D)

Verified step by step guidance

1. Understand that whether an object floats or sinks in water depends on the concept of density, which is mass per unit volume, not just mass or surface area alone.
2. Recall that the density of an object is given by the formula \(\rho = \frac{m}{V}\), where \(m\) is the mass and \(V\) is the volume of the object.
3. Recognize that water has a known density, often denoted as \(\rho_{water}\), which is approximately 1000 kg/m³ at standard conditions.
4. The key factor determining if an object floats is the comparison between the object's density and the density of water, expressed as the ratio \(\frac{\rho}{\rho_{water}}\).
5. If this ratio is less than 1, the object is less dense than water and will float; if it is greater than 1, the object is denser and will sink.