CAIE A-Level Physics 1.2.3 Checking Homogeneity with SI Base Units

Practise checking dimensional homogeneity with SI base units, finding inconsistent dimensions and using dimensional analysis to check formulas without proving them.

Exam points

Use SI base units to check that the dimensions on both sides of a physical equation are homogeneous.
Rewrite quantities in base-unit form and identify a missing or inconsistent dimension in a proposed relationship.
Use dimensional consistency as a check on a derived formula or calculated physical result, without treating it as proof of the numerical law.

[Maximum number: 2]

The density $\rho$ of the rock from which the pebble in (b) is composed is given by

\rho=\frac{M r^{n}}{k L}

where n is an integer and k is a constant, with no units, that is equal to 2.094 .

Use SI base units to show that n is equal to -2 .

$\mathrm{kg} \mathrm{m}^{-3}=\mathrm{kg} \times \mathrm{m}^{n} / \mathrm{m}$ or $\mathrm{kg} \mathrm{m}^{-3}=\mathrm{kg} \times \mathrm{m}^{n} \times \mathrm{m}^{-1}$

M1

-3=n-1 and (so) n=-2

A1

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1.2.3—SI base units to check the homogeneity of physical equations question 1