CAIE A-Level Physics AS 1.2.2 Derived Units As Products or Quotients of the Si Base Units and Use the Questions

Derive compound units as products or quotients of SI base units and use dimensional consistency to check Cambridge A Level Physics equations and calculations.

Exam points

Derive compound units as products or quotients of SI base units and use dimensional consistency to check physics equations and calculations.

[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 $F: \mathrm{kg} \mathrm{m} \mathrm{s}^{-2}$
units of r: m and units of $v: \mathrm{m} \mathrm{s}^{-1}$

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

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CAIE A-Level Physics AS 1.2.2 Derived Units As Products or Quotients of the Si Base Units and Use the Questions question 1