Question Detail
Question
A thin rod of mass M and length L has a moment of inertia about an axis perpendicular to it through its center given by I = (1/12) M L². Using the parallel axis theorem, what is its moment of inertia about a parallel axis through one end?
Correct Answer
Option A is the correct answer.
Detailed Explanation
The parallel axis theorem states I = I_cm + Mh², where h is the perpendicular distance between the two parallel axes. Here, the distance from the center to the end is h = L/2. Therefore, I = (1/12) M L² + M (L/2)² = (1/12 + 1/4) M L² = (1/3) M L².
Hint
The parallel axis theorem relates the moment of inertia about any axis to that about a parallel axis through the center of mass.