Physics 9702/52 — February/March 2021

A student investigates the vertical oscillations of a solid cylinder which floats in cooking oil. Fig. 1.1 shows a cylinder of radius $r$.

The student places the cylinder of mass $m$ in the oil. The cylinder is displaced vertically from its equilibrium position and released so that it oscillates. The period $T$ of the oscillations is determined.

A number of cylinders of different mass are available.

It is suggested that the relationship between $T$ and $m$ is

where $\sigma$ is the density of the oil and $K$ is a constant.

Design a laboratory experiment to test the relationship between $T$ and $m$.
Explain how your results could be used to determine a value for $K$.

You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.