2.2 Density
2.2.1 Density
Density is Mass per unit volume of a substance.
- Formula: Density =\( \frac{mass}{volume}\)
ρ =\( \frac{m}{V}\) - Units: Typically expressed in kilograms per cubic meter (\( \frac{Kg}{m³}\)) in the SI system.
- Common alternative unit: grams per cubic centimeter (\( \frac{g}{cm³}\)).
- Ensure consistent units for mass and volume when calculating density.
❓ Exam Question
0625/0972-Feb-Mar-22-2021-Q5
A small bottle has a mass of 20 g when empty. The volume of the bottle is 10\( \frac{c}{ m^3}\).
When full of liquid, the total mass is 150 g.
What is the density of the liquid?
Table below showing densities of different materials.
Density of Solids Compared to Gases:
Solids are more dense than gasses because for same volume, the molecules of solids are closely spaced as shown in figure
Volume Formulas:
Sometimes, when the volume of an object is not given, it can be calculated using a volume formula based on the shape of the object.
Figure: Diagram shows the formula of volume of different shapes.
❓ Exam Question
0625/0972/21-May-June-2019-Q5
The diagrams show four solid blocks with their dimensions and masses.
Which block has the greatest density?
Example:
A slab has a mass of 73kg and dimensions 0.90m ×0.5m ×0.2m. Calculate the density of the material from which slab is made?
Figure: Diagram showing a slab of known dimensions.
Solution:
Mass of slab = 73kg
Volume = 0.90m ×0.5m ×0.2m = 0.09m3
By using formula,
Density =\( \frac{m}{ V}\) =\( \frac{73}{ 0.09}\)
=811\( \frac{kg}{ m^3}\)