Answer & solution
Answer: (c) The weight of the fluid displaced
Correct Answer: The weight of the fluid displaced — Option (c)
Archimedes' Principle states that when a body is immersed (fully or partially) in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the body. Mathematical expression: Buoyant Force ( F_b ) = Weight of fluid displaced = ρ_fluid × V_displaced × g; where ρ_fluid = density of the fluid, V_displaced = volume of fluid displaced, g = acceleration due to gravity. Key implications: If the buoyant force exceeds the weight of the object, it floats; if the weight exceeds the buoyant force, it sinks; if they are equal, the object is in neutral buoyancy. Applications: Ship design, submarines (which control their depth by adjusting buoyancy), hot air balloons, hydrometers (used to measure the density of liquids), and determining the purity of gold (as Archimedes famously did for King Hiero II's crown).
Option (a) Its own weight — Incorrect: The buoyant force is NOT equal to the object's own weight (unless the object is in neutral buoyancy/floating); the buoyant force equals the weight of the FLUID DISPLACED, which may be more, less, or equal to the object's own weight.
Option (b) The volume of the body — Incorrect: The buoyant force is not equal to the volume of the body; volume is part of the calculation (buoyant force = density of fluid × volume displaced × gravity), but the buoyant force itself equals the WEIGHT (not volume) of fluid displaced. The candidate selected this incorrect option.
Option (d) The density of the fluid — Incorrect: The density of the fluid alone does not equal the buoyant force; density is one factor in calculating the buoyant force (along with volume displaced and gravity), but Archimedes' principle specifically states the buoyant force equals the WEIGHT of the fluid displaced.