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The centre of mass of a solid cone along the line from the centre of the base to the vertex is at:

1. one-fourth of the height
2. one-third of the height
3. one-fifth of the height
4. None of the above

Correct answer: one-fourth of the height

Solution

For a uniform solid cone, the centre of mass lies on the axis at a distance $h/4$ from the base. This is a standard result from integration or symmetry arguments.

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