In the context of buoyancy, does the volume of an object alone determine whether it will float or sink in a fluid?

• A. No, both the object's density $\rho$ and the fluid's density $\rho$_fluid are required to determine if it will float or sink.
• B. No, only the mass $m$ of the object determines whether it will float or sink.
• C. Yes, the volume $V$ of the object is the only factor that determines if it will float or sink.
• D. Yes, as long as the object has a large volume $V$, it will always float regardless of its density $\rho$.

Answer: (A)

Verified step by step guidance

1. Understand that whether an object floats or sinks depends on the relationship between the object's density and the fluid's density, not just the object's volume alone.
2. Recall the principle of buoyancy, which states that the buoyant force on an object submerged in a fluid equals the weight of the fluid displaced by the object. This force depends on the volume of fluid displaced and the fluid's density.
3. Express the object's density as \(\rho = \frac{m}{V}\), where \(m\) is the mass and \(V\) is the volume of the object.
4. Compare the object's density \(\rho\) with the fluid's density \(\rho_{fluid}\). If \(\rho < \rho_{fluid}\), the object will float; if \(\rho > \rho_{fluid}\), it will sink.
5. Conclude that volume alone does not determine floating or sinking; both the object's density (which depends on mass and volume) and the fluid's density must be considered.