Final answer:
To find the number of smaller disks needed in System B to match the moment of inertia of System A, calculate the moment of inertia for each type of disk and equate them. The calculation shows that four smaller disks are needed for System B to match the moment of inertia of two larger disks in System A.
Step-by-step explanation:
The question pertains to the comparison of moments of inertia for different systems of disks in Physics. We need to use the formula for the moment of inertia of a solid disk, which is I = MR², where M is the mass of the disk and R is its radius. For a disk with radius 2R, the moment of inertia would be I = M(2R)² = 4MR².
System A consists of two larger disks of radius 2R. Thus, the moment of inertia for System A is 2 × 4MR² = 8MR². System B has a combination of one larger disk and smaller ones. Since the moment of inertia for a single larger disk is 4MR², we have 4MR² + nMR² = 8MR², where n represents the number of smaller disks needed to match the moment of inertia of System A.
Solving for n, we get n = 8MR² - 4MR² over MR², which simplifies to n = 4. Thus, System B needs four smaller disks to have the same moment of inertia as System A.