The quantitative law giving the force of repulsion between two charges, which is basic to our present understanding of electricity and magnetism, was discovered by Coulomb using a torsion balance, a device he invented.
In that experiment, the charged object was a small ball on the end of a rod suspended horizontally by a long thin wire. The force exerted on the charge could be measured by how much it twisted the wire.
Coulomb found that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
This experiment uses a different method to verify part of Coulomb's law. We do not vary the charge, but we study how the force between charged objects varies with distance between them. One of the two objects is a roughly spherical dome of an electrostatic generator.
The other is a small light-weight pith ball hanging from a string. By knowing the mass of the pith ball, and doing some calculations based on the geometry involved, you will be able to determine both the force between the pith ball and the dome, and its distance from the center of the dome, repeating this for different distances.
Analyzing the data then allows you to find the dependence of the force on the distance from the center of the dome.
You might well wonder how we can get away with using the distance to the center of the electrically charged metal dome rather than to its outer surface. Wonder no longer! It is explained in the lab write up, which should be read well before attending the lab session.
The lab write up also calls for a derivation to be presented in your lab report, so it is best to solve that problem before the lab session.