9702 · 1.1

Physical quantities — practice questions

Practice and worked examples for 9702 Physical quantities. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

Show that the equation for kinetic energy, $E_k = \frac{1}{2}mv^2$ , is dimensionally homogeneous.

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Identify units for each term:
- Energy (E_k): Joules (J), which is kg m² s⁻²
- Mass (m): kilograms (kg)
- Velocity (v): meters per second (m s⁻¹)
Substitute units into the right-hand side (RHS) of the equation:
- RHS units = [kg] $\times [m s^{-1}]^{2}$
- RHS units = [kg] $\times [m^{2} s^{-2}]$
- RHS units = kg m² s⁻²
Compare RHS units with Left-hand side (LHS) units:
- LHS units (kg m² s⁻²) = RHS units (kg m² s⁻²)
Conclusion: Since the units on both sides are consistent, the equation is dimensionally homogeneous.

A ruler with millimetre divisions measures a length as 25.5 cm. State the absolute uncertainty for this single reading.

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Smallest division of the ruler = 1 mm = 0.1 cm.
Absolute uncertainty for a single $reading = \pm half of the smallest division$ .
Absolute $uncertainty = \pm \frac{1}{2} \times 0$ .1 $\text{ cm} = \pm 0$ .05 $\text{ cm}$ .
The length should be stated as 25.50 $\pm 0$ .05 $\text{ cm}$ .