center of mass

GCT

Please send the answer and explanation to GeneralChemistryTutor@hotmail.com, discussion of the problem is fine however don't ruin the fun by posting the answer.

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.

hint: if you are not able to solve it refer the problem to those whom you believe can.


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Gokul43201

Some clarifications :

1. Can we neglect the thickness of the tumbler compared to other lengths ? ie : is t << 4 cm ?

2. Are 12, 4 and 4.5 cm outside or inside dimensions ?

Unless there is some missing info in the problem, the solution appears to be independent of the thickness. So, one can do no harm by making the assumption stated in 1. If one makes this assumption, then 2 is irrelevant.