Physical Quantities, Units and Measurements
What the exam tests
This domain checks whether you can express measurements in SI base units, test dimensional consistency, combine uncertainties, and resolve vectors. Practical questions often use vernier calipers or a micrometer screw gauge, so the reading method and zero error matter.
Core rules
- SI base units: kg, m, s, A, K, mol, cd. Derived units are combinations; for example N = kg m s⁻² and J = kg m² s⁻².
- An equation is dimensionally homogeneous only if both sides have the same base dimensions. Dimensionless constants are invisible to dimensional analysis.
- For y = a ± b, add absolute uncertainties: Δy = Δa + Δb.
- For y = ab or a/b, add fractional uncertainties: Δy/y = Δa/a + Δb/b.
- For y = aⁿ, the fractional uncertainty is |n|Δa/a.
- A vector has magnitude and direction; resolve into perpendicular components and add components separately.
Worked example
A metal block has mass m = (54.2 ± 0.1) g and volume V = (20.0 ± 0.4) cm³. Find its density with uncertainty. ρ = m/V = 54.2/20.0 = 2.71 g cm⁻³. Fractional uncertainty = 0.1/54.2 + 0.4/20.0 = 0.00185 + 0.0200 = 0.0219. Absolute uncertainty = 0.0219 × 2.71 = 0.059 g cm⁻³. Result: ρ = (2.71 ± 0.06) g cm⁻³. The volume uncertainty dominates, so improving the volume measurement helps most.
Traps
Mixing mm and cm; applying the multiplication rule to addition; ignoring the sign of a zero error; quoting too many significant figures; giving a vector magnitude without its bearing; treating trigonometric ratios as having units.