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A solid cone and a solid hemisphere, each of mass M and base radius R, are placed coaxially. The flat circular face of the hemisphere is in contact with the base of the cone. Find the moment of inertia of the combined solid about the common symmetry axis YY'.
- 0.7 MR²
- 0.9 MR²
- 7/6 MR²
- 5/6 MR²
Correct answer: 0.9 MR²
Solution
Moment of inertia of a solid cone (mass M, base radius R) about its symmetry axis = (3/10)MR². Moment of inertia of a solid hemisphere (mass M, base radius R) about its symmetry axis = (2/5)MR² = (4/10)MR². Both share the same axis YY', so total MI = (3/10 + 4/10)MR² = (7/10)MR² = 0.7 MR².
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