Question

Two pieces of metal when immersed in a liquid have equal upthrust on them; then :
(A) Both pieces must have equal weights
(B) Both pieces must have equal densities
(C) Both pieces must have equal volumes
(D) Both are floating to the same depth

Answer 1

Buoyancy is the most frequent driving factor of convection currents, and it also applies to fluid mixes. The mathematical modelling is changed to apply to continuums in these situations, but the concepts remain the same. The spontaneous separation of air and water, or oil and water, are examples of buoyancy-driven flows. The centre of gravity of the displaced volume of fluid is the object's centre of buoyancy.

Complete answer:
The upward force exerted by a fluid against the weight of a partially or fully submerged item is known as buoyancy. The weight of the overlying fluid causes pressure to rise with depth in a column of fluid. As a result, the pressure at the bottom of a fluid column is larger than at the top. In the same way, the pressure at the bottom of an item submerged in a fluid is larger than the pressure at the top. The item is subjected to a net upward force as a result of the pressure differential. The force's magnitude is proportional to the pressure difference and is equal to the weight of the fluid that would otherwise fill the object's submerged volume, i.e. the displaced fluid. Archimedes' principle was named after Archimedes of Syracuse, who was the first to discover it in 212 BC. Archimedes' principle may be expressed in terms of forces for floating and submerged objects, gases, and liquids (i.e. fluids). Any object that is fully or partially submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object —with the caveats that the volume of displaced fluid is the volume of the object for a sunken object, and the weight of the displaced liquid is the weight of the object for a floating object on a liquid.
Simply put, buoyant force equals the weight of the displaced fluid.
When metal items are immersed in liquid (partially or completely), there is an upthrust equal to the weight of liquid displaced, which equals the weight that the metal objects have shown. As a result, the volume of the liquid equals the volume of the metal fragments.
Hence option C is correct.

Note:
The displaced fluid's weight is proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). The buoyancy force on an item is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g, in basic words. Items with higher volume have greater buoyancy among totally submerged objects of similar mass. Upthrust is another term for this.