A body floats in a liquid if the buoyant force is:

Correct — A, equal to its weight. A body that floats is at rest, and a body at rest has no net force on it. Only two vertical forces act — the weight pulling down and the buoyant force of the liquid pushing up — so the two must be equal in size. Archimedes' principle then tells you what that equality means physically: the buoyant force equals the weight of the liquid displaced, so a floating body displaces its own weight of liquid, no more and no less. That is why a steel ship floats although steel is denser than water: its hull encloses enough air for the whole vessel to displace a volume of water weighing as much as the ship. It also explains the self-correcting behaviour of a floating object — push it down and it displaces more liquid, the upward force exceeds the weight and it rises back until equality is restored.

• (b)less than its weight. — This is the sinking condition. With the upward push smaller than the downward pull there is a net downward force, and the body accelerates towards the bottom — the case of an iron nail in water.
• (c)greater than its weight. — This describes a body being pushed upward, such as a submerged cork released under water. It rises, but it cannot go on doing so; as it breaks the surface less of it is submerged, the displaced volume falls, and it settles where buoyancy equals weight.
• (d)zero. — Buoyancy is never zero for a body immersed in a liquid — the pressure on the lower surface always exceeds that on the upper. Zero buoyancy would leave only the weight, and the body would fall as if in vacuum.

Pressure in a fluid increases with depth, so the upward push on the bottom face of a submerged body is greater than the downward push on its top face. The difference is the buoyant force, or upthrust, and Archimedes' principle states that it equals the weight of the fluid displaced by the body. Whether a body floats or sinks therefore depends on the relation between its own density and the density of the fluid: less dense and it floats, denser and it sinks, equal and it stays wherever it is put.

The wording of these items is where marks are lost. 'A body floats' is a statement about equilibrium, so the answer must be an equality; 'a body rises', by contrast, would call for buoyancy greater than weight, and 'a body sinks' for buoyancy less than weight. Read the verb and match it to the sign of the net force. It is also worth keeping the density form and the force form of the criterion side by side: they are the same statement, since a body of density less than the liquid's can displace its own weight while still partly out of the liquid, whereas a denser one cannot do so even fully submerged.

• Buoyant force, or upthrust, arises because fluid pressure increases with depth, so the upward push on the lower surface exceeds the downward push on the upper.
• Archimedes' principle: the buoyant force on a body equals the weight of the fluid it displaces.
• A floating body is in equilibrium, so the buoyant force equals its weight and it displaces its own weight of liquid.
• Whether a body floats or sinks depends on the difference between the densities of the body and the liquid.
• A steel ship floats because its hull shape lets it displace a weight of water equal to its own, even though steel is denser than water.

• Reading 'floats' as 'rises' and choosing the greater-than option.
• Assuming a body floats because it is light; it is the density relative to the liquid, not the weight, that decides.
• Forgetting that buoyancy acts on a sinking body too — it merely loses to the weight.

As a one-line conceptual question on the floating condition, as an iron-nail-versus-ship comparison, or as a numerical asking for the upthrust on a fully immersed body.

• practice — not a real PYQ

  A body floating in a liquid displaces a volume of liquid whose weight is:

  • (a)half the weight of the body
  • (b)equal to the weight of the body
  • (c)twice the weight of the body
  • (d)independent of the weight of the body

  Answer(b) equal to the weight of the body — this is Archimedes' principle applied to the equilibrium of a floating body.

• practice — not a real PYQ

  An iron nail sinks in water while a ship made of iron floats. The best explanation is which one of the following?

  • (a)The ship is lighter than the nail
  • (b)The ship's shape lets it displace a weight of water equal to its own
  • (c)Sea water exerts no buoyant force on iron
  • (d)The nail has a higher density than the iron of the ship

  Answer(b) The ship's shape lets it displace a weight of water equal to its own — the hull encloses air, lowering the average density of the vessel below that of water.