Final answer:
This physics problem involves calculating the moment of inertia for a system of four identical rods arranged in a square and rotating about its diagonal, using relevant formulas and the parallel axis theorem.
Step-by-step explanation:
The question pertains to the moment of inertia of a system composed of four identical rods arranged to form a square, with rotation about the square's diagonal.
The moment of inertia I for a single rod about its end is given by I = ml²/3. However, the moment of inertia for the rod about its center, which is halfway along the length, is I = ml²/12 by using the parallel axis theorem or direct integration.
Considering the system of four rods arranged as a square, two rods have their centers aligned with the axis of rotation (the diagonal) and for each, the moment of inertia will be I = ml²/12. The other two rods will have rotation points at 1/4 and 3/4 of their lengths, not at their center or end.
Using the parallel axis theorem, the contribution of these two rods can be calculated and added to that of the first two rods. Performing these calculations leads us to the correct answer to the question.
The moment of inertia of the system of four identical rods about the diagonal of the square can be found by considering each rod individually and then adding up their individual moments of inertia.
Since each rod is identical, their moment of inertia about the diagonal of the square is the same.
The moment of inertia of a rod rotated around an axis through one end perpendicular to its length is given by ML²/3. Therefore, the moment of inertia of the system is (ML²/3) + (ML²/3) + (ML²/3) + (ML²/3) = (4/3)ML².