CAIE A-Level Physics 1.2.2 Derived Units in SI Base Units

Practise deriving units from SI base units, converting equivalent forms and checking equations or answers through dimensions and physical meaning.

Exam points

Express a derived unit as a product or quotient of SI base units, including the correct powers.
Use an appropriate named or derived unit for a syllabus quantity and convert consistently between equivalent forms.
Check a physical equation or calculated answer by tracing the derived unit and its dimensional meaning.

[Maximum number: 2]

The drag force $F_{\mathrm{D}}$ acting on a sphere falling through a liquid is given by

F_{\mathrm{D}}=6 \pi \eta r v

where r is the radius of the sphere,
v is the speed of the sphere in the liquid and
$\eta$ is a property of the liquid called the viscosity.

Show that the SI base units of viscosity are $\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}$ .

units of $F: \mathrm{kg} \mathrm{m} \mathrm{s}^{-2}$

C1

units of r: m and units of $v: \mathrm{m} \mathrm{s}^{-1}$

units of $\eta: \mathrm{kg} \mathrm{m} \mathrm{s}^{-2} /\left(\mathrm{m}^{\circ} \times \mathrm{m} \mathrm{s}^{-1}\right)=\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}$

A1

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1.2.2—Derived units as products or quotients of the SI base units and use the question 1