Whether an object will float or sink in a liquid, depends on

Whether an object will float or sink in a liquid, depends on

mass of the object only
mass of the object and density of liquid only
difference in the densities of the object and liquid
mass and shape of the object only
This question was previously asked in
UPSC NDA-1 – 2018
Whether an object floats or sinks in a liquid is determined by comparing the density of the object to the density of the liquid. According to Archimedes’ principle and the concept of buoyancy, an object will sink if its density is greater than the density of the liquid, float if its density is less than the density of the liquid, and be suspended if its density is equal to the density of the liquid. The difference in densities dictates the outcome. Options A, B, and D are insufficient as they do not solely or correctly identify the determining factor. Mass alone doesn’t account for volume, and while shape can influence *how* an object floats (by affecting the volume of liquid displaced before full submersion), the fundamental condition for sinking is based on the object’s average density relative to the liquid’s density.
– Buoyancy force is the upward force exerted by a fluid that opposes the weight of an immersed object.
– An object floats if the buoyant force is equal to or greater than its weight.
– The buoyant force is equal to the weight of the fluid displaced by the object.
– Floating/sinking is determined by comparing the density of the object (or its average density for irregularly shaped objects) to the density of the liquid.
Density is defined as mass per unit volume (ρ = m/V). The weight of an object is W_object = m_object * g = ρ_object * V_object * g. The maximum buoyant force when fully submerged is F_buoyant_max = W_liquid_displaced = ρ_liquid * V_object * g. The object sinks if W_object > F_buoyant_max, which simplifies to ρ_object > ρ_liquid. The object floats if W_object <= F_buoyant_max (partially or fully submerged), which simplifies to ρ_object <= ρ_liquid.
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