🌟 IGCSE Physics Topic 1.4: Density

🔹 1. Definition of Density

✅ Key Definition

Density (ρ) is defined as:

mass per unit volume

✅ Formula

Where:

• ( ρ ) = density (kg/m³ or g/cm³)
• ( m ) = mass (kg or g)
• ( V ) = volume (m³ or cm³)

🔹 2. Units of Density

Unit System	Density Unit
SI Units	kg/m³
Common Lab Units	g/cm³

🔁 Conversions to Remember

• 1 g/cm³ = 1000 kg/m³
• 1 kg/m³ = 0.001 g/cm³

🔹 3. Rearranging the Formula

You should be able to rearrange the formula:

📌 Exam Tip: Rearranging correctly is a very common exam skill.

🔹 4. Measuring Density

🧪 A. Density of a Liquid

Method

1. Measure mass of empty container
2. Measure mass of container + liquid
3. Find mass of liquid:
   
4. Measure volume using a measuring cylinder
5. Calculate density using formula

Example

Mass of liquid = 200 g
Volume = 100 cm³

🧱 B. Density of a Regular Solid

Method

1. Measure mass using a balance

2. Measure dimensions (length, width, height)

3. Calculate volume using geometry:

   

4. Use:
   

Example

Mass = 240 g
Dimensions = 4 × 3 × 2 cm

🪨 C. Density of an Irregular Solid (Displacement Method)

Condition: Object must sink

Method

1. Measure mass using a balance
2. Fill measuring cylinder with water (initial volume
3. Submerge object completely
4. Record new volume
5. Volume of object:
   
6. Calculate density

Example

Mass = 150 g
Initial volume = 50 cm³
Final volume = 70 cm³

🔹 5. Floating and Sinking

✅ Key Principle

An object floats or sinks depending on its density compared to the liquid.

Condition	Result
Object density < liquid density	Floats
Object density > liquid density	Sinks
Equal densities	Suspends (neutral buoyancy)

🧠 Explanation

• Floating happens because the liquid can support the object
• Sinking happens because the object is too dense

📌 Example

• Wood (≈ 0.6 g/cm³) in water (1.0 g/cm³) → floats
• Iron (≈ 7.8 g/cm³) in water → sinks

🔹 6. Floating of Liquids

✅ Rule

For liquids that do not mix:

• The less dense liquid floats on top
• The more dense liquid sinks

📌 Example

Liquid	Density
Oil	0.8 g/cm³
Water	1.0 g/cm³

👉 Oil floats on water

🧠 Key Idea

Liquids form layers based on density

🔹 7. Common Mistakes (Exam Focus ⚠️)

• ❌ Forgetting to subtract volumes in displacement
• ❌ Mixing up units (g/cm³ vs kg/m³)
• ❌ Using wrong formula rearrangement
• ❌ Not stating units in final answer
• ❌ Confusing mass with weight

🔹 8. Practical Skills Tips 🧪

• Read measuring cylinder at eye level (avoid parallax error)
• Use correct instruments:
  • Balance → mass
  • Measuring cylinder → volume
• Ensure object is fully submerged (no air bubbles)

🔹 9. Graph & Thinking Skills

Density Interpretation:

• High density = particles closely packed
• Low density = particles more spread out

🔹 10. Quick Summary 🧾

• Density = mass ÷ volume
• Units: kg/m³ or g/cm³
• Measure:
  • Liquid → measuring cylinder
  • Regular solid → dimensions
  • Irregular solid → displacement
• Floating depends on density comparison
• Less dense liquid floats on denser liquid

🔥 Final Exam Tips

• Always write the formula first
• Show working clearly
• Include units at every step
• Double-check calculations
• Use correct significant figures