IBM Ponder This #009 · January 1999

Consider a cylindrical drinking glass of uniform thickness, $12$ centimetres high and $4$ centimetres in radius. As water is poured into the glass, the center of mass of the glass and water together first moves lower and then higher. It is at its lowest when the water is $4.5$ centimetres deep.

What is the mass of the tumbler?

Hint. Ignore the edges. The glass has a bottom and a side but no top.

Bonus. Is it possible to construct a glass whose center of mass never drops as water is added? For this part, the glass may have any shape; it need not be cylindrical.

Solution

Best opened after a real attempt

Solution

To be added.