Quick questions on Physical quantities and SI units: base and derived units, prefixes and homogeneity - OCR A-Level Physics A

A base unit is defined independently; a derived unit is built from base units by the defining equation of the quantity. Because the whole of physics is internally consistent, expressing a derived unit in base units is just a matter of following the definition.

Other common results worth knowing: the pascal is $\text{kg m}^{-1}\text{s}^{-2}$ (force over area), the coulomb is $\text{A s}$ (current times time), and the volt is energy per unit charge, $\frac{\text{kg m}^2\text{s}^{-2}}{\text{A s}} = \text{kg m}^2\text{s}^{-3}\text{A}^{-1}$. Deriving these from definitions is more reliable than memorising them.

A physically valid equation must be homogeneous: every additive term has the same base units. To check, reduce each term to base units and compare. If they differ, the equation is certainly wrong. If they match, the equation is dimensionally possible, but homogeneity cannot detect a missing dimensionless factor such as $\frac{1}{2}$ or $2\pi$.

Express the joule in SI base units. [1 mark]

Write $0.000\,045\ \text{m}$ in standard form and in micrometres. [2 marks]

State what is meant by a homogeneous equation and one limitation of a homogeneity check. [2 marks]