Physics 9702/13 — May/June 2018

Background Concept

A physical quantity is something that can be measured. Any measurement must be expressed as:

• a number (the magnitude, e.g. 2.3), and
• a unit (e.g. (\text{m}), (\text{s}), (\text{kg}), (\text{V})).

Some physical quantities are vectors (they also need a direction), but direction is not part of the definition of “physical quantity” in general, because many physical quantities are scalars.

Understanding the Question

The question asks for the best description of a physical quantity in general (not specifically a vector or specifically a scalar). So the correct statement must always be true for any measurable quantity.

Approach

Use the definition: measured quantities must have a magnitude and a unit. Then check which option matches that, and reject options that incorrectly require direction or omit unit/magnitude.

Step-by-Step Reasoning

• Option A: “magnitude and direction but no unit” describes a vector-like idea, but missing a unit makes it not a valid physical measurement.
• Option B: “magnitude and a unit” matches the definition of a physical quantity (e.g. (5.0\ \text{m}), (2.1\ \text{A})).
• Option C: “magnitude but no direction” describes a scalar, but still misses the essential requirement that it must have a unit.
• Option D: “unit but no magnitude” is impossible as a measurement because you cannot specify an amount without a number.

Therefore the correct choice is B.

Key Takeaways

• A physical quantity is expressed as number + unit.
• Direction is only required for vector quantities, not for all physical quantities.

Common Mistakes

• Thinking “physical quantity” means “vector quantity”, and choosing an option that includes direction.
• Forgetting that a measurement without a unit is incomplete.

Things to Be Careful About

• The word “best” signals a general definition, not a special case (scalar/vector).
• Units are essential even if sometimes omitted informally; in exams, the correct description must include them.