3. A solid uniform sphere of radius R and mass M has arotational inertia about a

Question

3. A solid uniform sphere of radius R and mass M has arotational inertia about a diameter that is given by (2/5)MR2. A light string of length 3R is attached tothe surface and used to suspend the sphere from the ceiling. Its rotational inertia about thepoint of attachment at the ceiling is: A) (2/5)MR2 B) 9MR2 C) 16MR2 D) 47/5MR2 E) (82/5)MR2 3. A solid uniform sphere of radius R and mass M has arotational inertia about a diameter that is given by (2/5)MR2. A light string of length 3R is attached tothe surface and used to suspend the sphere from the ceiling. Its rotational inertia about thepoint of attachment at the ceiling is: A) (2/5)MR2 B) 9MR2 C) 16MR2 D) 47/5MR2 E) (82/5)MR2

Explanation / Answer

Required rotational inertia I = ( 2/ 5 ) M R ^ 2 +M ( 4R ) ^ 2 Since from parallel axis theorem , I = I g + M x ^ 2 where I g = moment of inertia about a center ofgravity            x = distance of the point from center og gravity = 3R+ R = 4R So, I = ( 82 / 5 ) M R ^ 2

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