Physics 9702/12 — February/March 2023

Background Concept

A physical quantity is something that can be measured and expressed as:

• a numerical value (magnitude), and
• a unit (e.g. (\text{m}), (\text{s}), (\text{kg}), (\text{N})).

This is why measurements are normally written in the form

$$\text{quantity} = (\text{number}) \times (\text{unit}).$$

Understanding the Question

You are given four different ways of writing information (a pure number, a unit word, a number with a unit, and a percentage). The question asks which one correctly represents a physical quantity in the usual physics sense.

Approach

Check each option for the two required components:

1. Is there a number?
2. Is there an associated unit that tells what is being measured?

Choose the option that clearly includes both.

Step-by-Step Reasoning

• A: (3.0)

  • Has a number but no unit, so it is not a complete physical quantity.

• B: kilogram

  • This is a unit only, with no numerical value, so it is not a complete physical quantity.

• C: (7.0\ \text{N})

  • Has a number (7.0) and a unit (\text{N}) (newton, a unit of force), so it is a physical quantity.

• D: (40%)

  • Although percentage can be used to express ratios (e.g. efficiency), in this context it is not given as a standard physical unit attached to a measured quantity (it is a dimensionless ratio written in percent form). The clearly correct “number + unit” measurement is option C.

Therefore the answer is C.

Key Takeaways

• A physical quantity must be expressed with magnitude and unit.
• “Unit only” or “number only” is incomplete.

Common Mistakes

• Choosing A because it “looks like a measurement” but forgetting the unit.
• Choosing B because it is a familiar SI base unit, but forgetting a numerical value is required.
• Confusing a percentage with a physical unit in this definition-style question.

Things to Be Careful About

• In MCQs like this, Cambridge typically expects the definition: numerical value + unit.
• Even when something is dimensionless (like a ratio), it is often still written with a defined quantity name (e.g. (\eta = 0.40) or (40%)), but here the safest identification of a physical quantity is the one explicitly written with a standard unit ((\text{N})).