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

• A. Only the $V$ (volume) of the object matters, not its $m$ (mass).
• B. No, both the object's $\rho$ (density) and the fluid's $\rho$ (density) are required to determine if it will float or sink.
• C. Only the temperature of the fluid determines if the object will float or sink.
• D. Yes, the object's $m$ (mass) alone determines whether it will float or sink.

Answer: (B)

Verified step by step guidance

1. Understand that whether an object floats or sinks in a fluid depends on the relationship between the object's density and the fluid's density, not just the object's mass.
2. Recall that density (\rho) is defined as mass (m) divided by volume (V), expressed as \(\rho = \frac{m}{V}\).
3. Apply Archimedes' principle, which states that the buoyant force on an object submerged in a fluid equals the weight of the fluid displaced by the object.
4. Compare the object's density to the fluid's density: if the object's density is less than the fluid's density, it will float; if greater, it will sink.
5. Conclude that both the object's density and the fluid's density are necessary to determine floating or sinking, so mass alone is insufficient.