Buoyancy & Archimedes' Principle

• Buoyant force (upthrust) — upward force exerted by fluid on immersed object.
• Archimedes' principle — buoyant force = weight of fluid displaced.
• Floating vs sinking — depends on comparison of object density with fluid density.
• Applications: ships, submarines, hot-air balloons, hydrometer.

1. Upthrust — acts upward; equal to weight of displaced liquid (Archimedes).
2. F_b = ρ_fluid × V_displaced × g (NCERT form).
3. Float — if ρ_object < ρ_fluid (or weight ≤ buoyant force).
4. Sink — if ρ_object > ρ_fluid.
5. Apparent weight in fluid = true weight − buoyant force.
6. Diagram (text) — iron nail sinks in water; iron ship floats (average density < water).
7. NCERT Ch. 10 — stone in water feels lighter; Eureka story (historical).
8. Real world — swimming; dead sea high salinity → easier float; ice floating on water.

A block displaces 0.5 m³ of water. Find buoyant force (ρ_water = 1000 kg/m³, g = 10 m/s²).

Step 1 — Weight of displaced water = m × g = (ρ × V) × g
Step 2 — m = 1000 × 0.5 = 500 kg
Step 3 — Buoyant force = 500 × 10 = 5000 N upward
Step 4 — If block weighs 4000 N, it floats (upthrust > weight).
Step 5 — If block weighs 6000 N, it sinks (upthrust < weight).

• Thinking heavier objects always sink (depends on density and volume displaced).
• Misconception: buoyant force depends on depth alone (depends on volume submerged).
• Confusing mass of object with mass of displaced fluid.
• Forgetting partial immersion — only submerged volume counts.
• Assuming floating object has zero buoyant force (equals weight when floating).

• State Archimedes' principle.
• Why does a ship float though iron sinks?
• A 10 N stone weighs 6 N in water. Find buoyant force.
• What determines whether an object floats or sinks?

Open the Practice tab for graded questions on Buoyancy & Archimedes' Principle.