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

A student investigated the viscosity of olive oil at different temperatures using a steel sphere of radius $r$.

Describe how the student can make measurements of the steel sphere to determine its radius accurately.

Explain how the student can ensure that Stokes' law will apply to the steel sphere as it falls through the olive oil.

The student dropped the steel sphere into a tall cylinder of olive oil, as shown, and timed the sphere as it fell through the oil at terminal velocity.

The student placed two rubber bands around the cylinder and started a stopwatch when the sphere passed the first band and stopped it when the sphere passed the second band.

The student recorded the time $t$ for the ball to fall through a distance of $21.0\text{ cm}$ and repeated this for three different temperatures. They calculated the viscosity $\eta$ at each temperature using the formula

$\eta =\frac{2r^{2}g\left({\rho }_s-{\rho }_o\right)}{9v}$

radius of steel sphere $r=2.2\text{ mm}$
density of steel ${\rho }_s=7800{\text{ kg m}}^{-3}$
density of olive oil at 20 °C ${\rho }_o=920{\text{ kg m}}^{-3}$

Their results are shown in the table.

The student concluded that the viscosity of olive oil decreases linearly with temperature.

Criticise the student's investigation and conclusion.