Question Detail
Question
A uniform rod of length L and mass M rotates about an axis perpendicular to the rod and passing through its center. Its moment of inertia is (1/12)ML². Using the parallel-axis theorem, its moment of inertia about a parallel axis through one end is
Correct Answer
Option D is the correct answer.
Detailed Explanation
The parallel-axis theorem states I = I_cm + MD². Here, I_cm = (1/12)ML², and the distance D from the center of mass to the end of the rod is L/2. Therefore, I = (1/12)ML² + M(L/2)² = (1/12)ML² + (1/4)ML² = (1/3)ML².
Hint
Apply the parallel-axis theorem. The distance D is the separation between the center of mass axis and the new axis, which is half the length of the rod.