A baton consists of a nearly massless rod of length L and two spheres attached to the ends of the rod,whose masses are each M and whose centers are separated by L.The spheres have radius R.If the sphere radius R is negligible compared to the length L,what is the moment of inertia of the baton about an axis perpendicular to its length and passing through its center? A)2ML² B)ML² C)(1/2)ML² D)(1/4)ML²

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Quizplus · Accepted Answer

Since the radius is negligible compared to the length, we can consider the baton as a thin rod with two point masses attached to it. The moment of inertia of a thin rod of length L and mass M about an axis perpendicular to its length and passing through its center is (1/12)ML^2. Each sphere has a moment of inertia of (2/5)MR^2 about an axis passing through its center and perpendicular to its surface. Using the parallel axis theorem, the moment of inertia of each sphere about an axis passing through the center of the rod is (2/5)MR^2 + (1/4)ML^2. Therefore, the moment of inertia of the baton about an axis perpendicular to its length and passing through its center is (1/12)ML^2 + 2[(2/5)MR^2 + (1/4)ML^2] = (1/2)ML^2 + (4/5)MR^2. Since R is negligible compared to L, the moment of inertia becomes (1/2)ML^2, which is option C.

A Baton Consists of a Nearly Massless Rod of Length