IB Physics HL S1.3.4 Uncertainties Questions

Analyse HL random and systematic uncertainties, combining percentage uncertainties and reporting measurements with appropriate precision.

[Maximum number: 4]

A group of students is trying to determine the density and the viscosity of a liquid.

To determine the density, they use a balance to read the mass m of a sphere in air and immersed in the liquid.

They use a sphere of volume $V=1.827 \times 10^{-7} \mathrm{~m}^{3}$ .
The readings are $m_{\text {air }}=1.427 \mathrm{~g}$ in air and $m_{\text {immersed }}=1.208 \mathrm{~g}$ in the liquid.
The readings are different due to buoyancy. The buoyancy force $F_{\mathrm{b}}$ is given by

F_{\mathrm{b}}=\rho V g

where V is the volume of the sphere and $\rho$ is the density of the liquid.

They repeat the experiment several times and estimate an average for

v_{\mathrm{t}}=(0.71 \pm 0.05) \mathrm{ms}^{-1}

They use the equation

\eta=\frac{m_{\mathrm{air}} g-\rho V g}{6 \pi r v_{\mathrm{t}}}

where
r= radius of the sphere,
$v_{\mathrm{t}}=$ terminal velocity of the sphere,
$\eta=$ viscosity of the liquid.
The radius r of the sphere is 3.520 mm .

Calculate the viscosity of the liquid and its absolute uncertainty. Ignore uncertainties in the mass, radius and volume of the sphere. Give your answer in the form $\eta \pm \Delta \eta$ , to an appropriate number of significant figures, including units.

$\begin{aligned} \eta=0.2512 7 \% \text { OR } 0.02 \eta=0.25 \pm 0.02 \text { Pa s OR } \mathrm{kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1} \end{aligned}$

MP1 and MP2 are for the calculations, accept any number of SF,

MP3 is for the matching precision of the value and its uncertainty. ECF may apply but uncertainty may only have 1 SF .

Allow other suitable units such as $\mathrm{Nm}^{-2} \mathrm{~s}$

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IB Physics HL S1.3.4 Uncertainties Questions

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