Question 06/98
FLOATING BODIES OF EQUILIBRIUM
Stanislav Ulam asked (in "The Scottish Book")
whether a sphere is the only solid of uniform density
which will float in water in any position. We ask a simpler, two-dimensional,
question: Consider a long log of circular cross-section; it will, obviously, float
in any position without tending to rotate. (Of course, the axis of the log is
asumed to be parallel to the water surface.)
(a) Are there any additional cross-section shapes such that the log will float in any
position if the density of the floating body is 0.5 gm/cm3?
(b) Are there any shapes for some other (predefined) values of the density? (Of course,
we assume that the given density is smaller than the density of water.)
(c) Are there any shapes, besides the circle, which will float in any position
independent of the density of the material?
Partial answers to the question are welcome.
A related question appeared in Feb. 98
and was solved.
Back to "front page"