Final answer:
The question involves calculating the moment of inertia for two different systems of disks to determine how many smaller disks must be present in one system to match the moment of inertia of the other. By setting the equations for the moments of inertia of the two systems equal to each other and solving for the number of smaller disks, we find that system B must contain 4 smaller disks.
Step-by-step explanation:
The question pertains to the concept of the moment of inertia in physics, which is a measure of an object's resistance to changes in its rotational motion. The comparison of two systems' moments of inertia can be solved by using the formula for the moment of inertia of a disk, which is ½MR², where M is the mass of the disk and R is its radius.
For system A, which consists of two larger disks, each with radius 2R, the combined moment of inertia is 2 times ½M(2R)², yielding a total moment of inertia of 4MR².
For system B, which includes one larger disk and several smaller disks, the moment of inertia can be expressed as ½M(2R)² plus the sum of the moments of inertia of the smaller disks, each of which has a moment of inertia of ½MR². If we denote the number of smaller disks in system B as x, the total moment of inertia for system B is ½M(2R)² + x(½MR²).
Setting the moments of inertia of system A and B equal to each other, we have:
4MR² = ½M(2R)² + x(½MR²)
This simplifies to:
4MR² = 2MR² + ½xMR²
Which further simplifies to:
2MR² = ½xMR²
Now we solve for x, which represents the number of smaller disks:
4 = x
Therefore, the answer is that system B must consist of 4 smaller disks, each with radius R, to have a moment of inertia equal to that of system A, which consists of two larger disks with radius 2R.