Where is the center of gravity located along the central radius of a solid hemisphere 3r_________________?
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Answer: D. at distance — from the plane base or
Explanation
The center of gravity of a solid hemisphere is located at a specific distance along its central radius from the plane base. Integration of mass moments across the hemispherical volume yields a centroid located precisely at three-eighths of the radius. The geometric asymmetry of a hemisphere shifts its center of gravity closer to the flat circular base than its curved apex. The center of gravity represents the average location of the weight distribution of a three-dimensional physical body. Calculations for standard geometric centroids utilize definite integrals balancing first moments of volume about coordinate axes. For a solid hemisphere of radius r, the centroidal distance from the flat base equals three-eighths of r.
Other fractional distances along the central radius fail to satisfy the volumetric integration required for a solid hemisphere. The center of gravity is never located at the outermost curved apex of the solid hemispherical body. Centroid positions depend strictly on geometric dimensions and do not vary arbitrarily with material density in uniform objects.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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