Final answer:
The student's question involves calculating the moment of inertia for different configurations of disks and marbles, using equations and theorems from physics, specifically the parallel-axis theorem for calculating moments of inertia not centered on the axis of rotation.
Step-by-step explanation:
The question involves the concept of moment of inertia, which is a measure of an object's resistance to changes in its rotational motion. In physics, the moment of inertia depends on the mass distribution of an object relative to the axis of rotation. Calculations often involve summing the products of mass elements and the square of their distance from the axis of rotation. For more complex shapes and mass distributions, formulas and theorems such as the parallel-axis theorem are used.
The question provided gives scenarios about disks with marbles and rods, and their respective moments of inertia. The moment of inertia for a solid disk can be calculated as MR² when rotating about an axis through its center, but alterations have to be made if the axis of rotation is not through the center. The parallel-axis theorem is used in such cases, which states that the moment of inertia about a parallel axis is equal to the moment of inertia about the center of mass plus the product of the mass and the square of the distance between the two axes.
For the comparison between systems A and B with different sized disks, the moment of inertia for system A consists of two larger disks with radius 2R and for system B involves one larger disk and multiple smaller disks with radius R. The total moment of inertia for system B will equal that of system A when enough smaller disks are added such that the sum of their individual moments of inertia equals the moment of inertia of the missing larger disk. So, it becomes a problem of solving an equation for the number of smaller disks needed for system B to have the same moment of inertia as system A.