A student notices that a label on a bottle of shampoo gives its volume in millilitres but does not state the mass of the shampoo inside. The student says: 'Volume and mass are both scalar quantities, so they are basically the same type of measurement.' Explain why the student's statement is incorrect, and describe the difference between a scalar quantity and a vector quantity.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A student is reading labels on bottles in a supermarket and makes a comment about physical quantities printed on the packaging.
Model answer (5 marks)
Both mass and volume are scalar quantities – they have only magnitude and no direction.
However, being scalars does not mean they are the same type of measurement. Mass measures the amount of matter in an object, whereas volume measures the space that object occupies. They are different physical properties.
Thus the student’s statement is incorrect: although mass and volume are both scalars, they are not the same quantity.
A scalar quantity has magnitude only (no direction). A vector quantity has both magnitude and direction.
However, being scalars does not mean they are the same type of measurement. Mass measures the amount of matter in an object, whereas volume measures the space that object occupies. They are different physical properties.
Thus the student’s statement is incorrect: although mass and volume are both scalars, they are not the same quantity.
A scalar quantity has magnitude only (no direction). A vector quantity has both magnitude and direction.
Examiner tips
- State that mass and volume are scalars, then explain they measure different properties; this shows understanding of the difference.
- Use the exact terms ‘scalar’ and ‘vector’ and give the definition of each.
- Show the distinction between ‘same type’ and ‘same quantity’ to earn full marks.
Common mistakes
- Confusing scalar with vector; claiming mass is a vector.
- Saying mass and volume are identical because they are scalars.
- Omitting the definition of a vector quantity (magnitude + direction).
Mark scheme (5 marks)
- A scalar quantity has magnitude only (no direction)
- A vector quantity has both magnitude and direction
- The student is correct that both mass and volume are scalar quantities / both have no direction
- Mass and volume measure different physical quantities / mass measures the amount of matter whereas volume measures the space an object occupies
- Being the same type (scalar) does not mean they are the same quantity / scalar vs vector classification does not determine what physical property is measured
Key terms in this question
scalar quantity · vector quantity · mass
Related
- All OCR A-Level Physics B: Advancing Physics (H557) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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