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Ponder This

January 1999

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Ponder This Challenge:

When adding a new tumbler to your collection, you wish to record its mass, but have only the following information available. Given a cylindrical drinking glass, of uniform thickness, 12 centimeters high and 4 centimeters in radius. The location of the center of mass of the glass and water together depends on the depth of the water.
As you pour water into the glass, the center of mass moves lower, then moves higher. The center of mass is at its lowest when the water is 4.5 centimeters deep. What is the mass of the tumbler? Hint: Ignore the edges. The glass has a bottom and a side but no top. Bonus question: Is it possible to construct a glass such that the center of mass never drops when you add water? For this part the glass can have any shape you wish; it need not be cylindrical. FYI: Although this problem may appear simple at first, the solution is actually fairly complex.

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Challenge: 01/01/99 @ 12:00 AM EST
Solution: 02/01/99 @ 12:00 AM EST
List Updated: 02/01/99 @ 12:00 AM EST

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