Final answer:
Without information about the pivot point and object masses, it is impossible to definitively determine where small-sized objects should be placed on the beam to achieve balance.
Step-by-step explanation:
The placement of small-sized objects on a uniform 9.00 kg plastic beam that is 3.00 m long to achieve balance depends on the distribution of mass and the location of the fulcrum or pivot point. Assuming the pivot point is at the center of the beam, placing small objects at the center will keep the beam balanced. If the pivot is not at the center, then placing objects either at one end or both ends must be done in a way that considers the torque caused by the objects' weight around the pivot point. In the absence of information about the location of the pivot point or the masses of the objects, it is not possible to determine the exact placement without further details.