Density of materials: mass, m, in kilograms, kg

The idea

Mass measures the amount of matter in an object and is measured in kilograms (kg). In density calculations, mass is the numerator when using ρ = m ÷ V, so a block with mass 2.4 kg and volume 0.003 m³ has density 2.4 ÷ 0.003 = 800 kg/m³. Mass is not the same as weight: weight is a force in newtons and depends on gravitational field strength, whereas mass in kg stays the same everywhere. When recording or using mass, convert grams to kilograms by dividing by 1000, for example 450 g = 0.45 kg. Always label the quantity with its symbol m and its unit kg, and check that the value is reasonable for the object being described.

What earns the marks

• States that mass is measured in kilograms (kg) and uses the symbol m correctly in equations.
• Converts masses given in grams to kilograms by dividing by 1000 before substituting into ρ = m ÷ V.
• Distinguishes mass in kg from weight in N, recognising that weight depends on gravitational field strength.
• Uses mass as the numerator in the density equation and keeps the unit kg consistent with volume in m³ to give density in kg/m³.
• Reads a balance or scale correctly and records mass to an appropriate precision with the unit kg.

Common mistakes and how to put them right

• Writing mass in grams when the equation requires kilograms.

  Put it right by dividing the gram value by 1000 before calculating density.

• Confusing mass with weight and giving the unit N.

  Put it right by stating that mass is in kg and weight is a force in N.

• Forgetting to include the unit kg with a numerical answer.

  Put it right by writing the unit after the value, for example 2.4 kg.

Exam tips

• Underline the mass value and its unit in the question, then convert to kg immediately if it is in g.
• Write the density equation with mass as the subject before substituting numbers, so the role of m is clear.
• Check that the final density unit is kg/m³ when mass is in kg and volume is in m³.