Physics 9702/11 — October/November 2020

Background Concept

A physical quantity is something that can be measured and expressed as a numerical value multiplied by a unit. For example, length can be written as $2.0\ \text{m}$ and time as $5.0\ \text{s}$. Derived quantities also have units built from base units, e.g. density in $\text{kg m}^{-3}$.

Some quantities in physics are dimensionless (ratios), but in this syllabus context the key identifying feature being tested is whether the quantity is expressed with an SI unit.

Understanding the Question

You are given four named quantities. You must pick which one is a (measurable) physical quantity in the sense of being expressible with a unit.

So you should check: does each option correspond to something you would write with units?

Approach

Go through each option and ask:

1. Is it a measured quantity (not just an identifying label)?
2. Does it have an SI unit (base or derived)?

The only option with a clear derived SI unit should be chosen.

Step-by-Step Reasoning

• A atomic number: this is the number of protons in a nucleus. It is an integer used to identify the element, so it is a pure count with no unit.

• B efficiency: defined by

$$\text{efficiency} = \frac{\text{useful output energy (or power)}}{\text{input energy (or power)}}$$

This is a ratio, so units cancel and it is dimensionless.

• C number density of charge carriers: number density means “number per unit volume”. Its unit is

$$\text{m}^{-3}$$

This is a derived SI unit, so it is clearly a physical quantity.

• D strain: defined by

$$\text{strain} = \frac{\Delta L}{L}$$

This is also a ratio of two lengths, so it is dimensionless.

Therefore the only option that is (unambiguously) a physical quantity with units is C.

Key Takeaways

• Physical quantities are measurable and (in this definition) expressed using units.
• Many “definition by ratio” quantities (efficiency, strain) are dimensionless because units cancel.
• Number density has unit $\text{m}^{-3}$, so it is a standard derived physical quantity.

Common Mistakes

• Choosing strain because it appears in formulae: it is commonly used, but it is dimensionless.
• Choosing efficiency because it is often written as a percentage: a percentage is still dimensionless.
• Treating atomic number as a measurable quantity with units: it is an identifying count, not a measured physical quantity in this context.

Things to Be Careful About

• Check whether units cancel in a definition (ratios often give dimensionless quantities).
• Do not confuse “important in physics” with “has units”: dimensionless parameters can be important but may not fit the definition being tested here.