Density, Mass & Volume
Definition of Density
Density is the
mass per unit volume of a substance.
ρ = m / V
Units: g/cm³ or kg/m³; 1 g/cm³ = 1000 kg/m³.
Subtopics
- Density of a liquid
- Density of a regular solid
- Density of an irregular solid (displacement)
- Floating or sinking
Mass & Weight
Mass: quantity of matter (scalar), measured by balance (kg).
Weight: gravitational force W = mg (vector), measured by Newton meter (N).
Gravitational field strength g = W/m (N/kg).
Density of a Liquid
- Mass of empty cylinder m₁.
- Add volume V of liquid; mass m₂.
- Mass of liquid
= m₂ − m₁. ρ = (m₂ − m₁)/V.
Keep eye level to avoid parallax.
Density of a Regular Solid
- Measure dimensions → compute volume.
- Weigh mass m;
ρ = m/V.
| Shape | Volume |
|---|---|
| Cube | l³ |
| Cuboid | l×b×h |
| Cylinder | πr²h |
| Sphere | 4/3 πr³ |
| Cone | 1/3 πr²h |
Density of an Irregular Solid (Displacement)
- Weigh object (mass m).
- Use a displacement can → collect displaced water in measuring cylinder.
- Volume of object = volume of displaced water.
ρ = m/V.
Avoid trapped air bubbles → they inflate the measured volume.
Float or Sink?
- Object density < fluid → floats (top layer if immiscible).
- Object density > fluid → sinks.
Summary Table
| Quantity | Definition | Formula | Unit | Type |
|---|---|---|---|---|
| Mass | Amount of matter | – | kg | Scalar |
| Weight | Gravitational force | W = mg | N | Vector |
| g | Force per unit mass | g = W/m | N/kg | Vector |
| Density | Mass per volume | ρ = m/V | kg/m³ | Scalar |
Always convert units correctly (g↔kg, cm³↔m³).