IBM Research | Ponder This | January 1999 challenges

# Ponder This

## January 1999

<<December January February>>

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.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

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