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A toy is made of a solid sphere attached to the base of a solid cone of the same base radius. The density of the sphere material is 12 times that of the cone. Using the fact that the centre of mass of a cone of height h lies at h/4 from its base, where is the centre of mass of the whole toy located?

1. At the junction of the sphere and the cone
2. At the centre of the sphere
3. At a point h/2 of the cone height above the base
4. At a point h/4 from the base of the cone

Correct answer: At the junction of the sphere and the cone

Solution

The much denser sphere dominates the mass distribution, so the weighted mean of the two centres of mass falls at the interface where the sphere meets the cone.

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