Floating and Sinking -The Role of Density

📚 Key Concepts

🔹 Real-Life Example: Oil floats on water because its density (~0.8 g/cm³) is lower than that of water (1 g/cm³). A coin sinks in water but floats in mercury because mercury is much denser (13.6 g/cm³). Ice floats in water due to its lower density.

🔹 Density is the mass per unit volume of a substance.

🧪 Important Formulas

• 🔸 Floating and Sinking Rules:
  • Object floats: When density of object < density of fluid
  • Object sinks: When density of object > density of fluid
  • Neutral buoyancy: When densities are equal

• 🔸 Mathematical Formula:
  ρ = m / V
  Where:
  • ρ = Density (kg/m³)
  • m = Mass (kg)
  • V = Volume (m³)

🔍 Advanced: Relation Between Upthrust and Gravity

For floating objects:
ρ(fluid) × V(submerged) × g = ρ(object) × V(total) × g

🔹 Examples

• 🛢️ Oil on Water: ρ(oil) < ρ(water)
• 🪙 Coin in Mercury: ρ(coin) < ρ(mercury)
• ❄️ Ice in Water: ρ(ice) = 0.92 g/cm³ < ρ(water)