Buoyancy & ArchimedesJEE Main

Float, sink and apparent weight — interactive Physics simulation for IIT-JEE.

Concept

Archimedes' principle: a submerged object feels an upward buoyant force equal to the weight of fluid it displaces. Compare densities to predict the outcome — lighter than the fluid floats, heavier sinks.

Key formula

F_B = \rho_{fluid}\,V_{disp}\,g, \qquad \text{float fraction} = \frac{\rho_{object}}{\rho_{fluid}}

Derivation

The pressure on the bottom of a submerged body exceeds that on top by $\rho_{fluid}\,g\,h$ , giving a net upward force $F_B = \rho_{fluid} V g$ .

A floating object sinks until the displaced weight equals its own, so the submerged fraction is $\rho_{object}/\rho_{fluid}$ — which is why ~90% of an iceberg hides underwater.

Scenarios to explore

Buoyancy & Archimedes — Float, sink, submerged fraction & apparent weight.

Real-world applications

Ship and submarine design (ballast).
Hydrometers measuring liquid density.
Hot-air balloons (buoyancy in air).

JEE exam tips

Apparent weight = real weight − buoyant force (loss of weight in a fluid).
Float fraction $\rho_{obj}/\rho_{fluid}$ — ice in water floats with ~10% above the surface.

Common mistakes

Using the object's total volume for a floating body — only the submerged part displaces.
Forgetting buoyant force depends on the fluid density, not the object's.
Thinking heavier objects always sink — it's density, not weight, that decides.

Exam traps to avoid

A fully submerged object displaces its whole volume regardless of depth.
In mercury ( $\rho = 13600$ ), even iron ( $\rho \approx 7900$ ) floats.