Density, Upthrust & Viscous Drag (Edexcel A Level Physics)

Topic Questions

3 marks

Genuine crystal balls are made from clarified quartz rather than glass.

A student was given a small crystal ball and wanted to know whether it was genuine.

The mean diameter of the crystal ball was measured to be 5.06 cm and the mass of the crystal ball was measured to be 175 g.

Show that the density of the material of the crystal ball is about 2600 kg m⁻³.

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6 marks

The student measured the diameter of the crystal ball using vernier calipers with a resolution of 0.01 cm.

She measured the mass of the crystal ball using a balance with a resolution of 1 g.

The table gives the densities of clarified quartz and glass.

Determine whether the crystal ball was genuine.

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2 marks

Raindrops of different sizes fall with different terminal velocities through air.

The table shows the measured value of the terminal velocity for raindrops of different sizes.

Derive, using Stokes’ law, the following expression for the terminal velocity v of a spherical raindrop in terms of its radius r.

$v = \frac{2 g ρ r^{2}}{9 η}$

where $ρ$ is the density of rainwater and $η$ is the viscosity of air.

You should ignore upthrust.

How did you do?

2 marks

Show that the expression given in (a) produces a value of about 800 m s^-1 for the terminal velocity of a large raindrop.

$ρ$ = 1.0 × 10³ kg m^-3
$η$ = 1.8 × 10^-5 Pa s

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3 marks

Explain whether Stokes’ law is suitable for calculating the terminal velocity of raindrops.

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