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        riddles >> easy >> Easy: Glass half full
        
(Message started by: jabhiji on Jan 29^th, 2003, 7:05pm)

Title: Easy: Glass half full
Post by jabhiji on Jan 29^th, 2003, 7:05pm

All one needs is a rotating turntable whose RPM can be increased to any desired value. Place the cylinder on the table so that their axes coincide.

When the cylinder rotates, the free surface of the water will become a paraboloid of revolution. More interesting, the rise of the surface at the edge will be exactly equal to the dip at the axis.

At a high enough RPM, if the cylinder were exactly half full to begin with, the dip will just touch the cylinder bottom while the rise at the edge will be on the verge of spilling water outside.

If it were (more/less) than half-full, the water will spill out (before/after) the dip touches the cylinder bottom.

Title: Re: Easy: Glass half full
Post by ThatGirlLooksTasty on Jan 30^th, 2003, 12:19am

Umm... the problem says the room is empty which means it probably doesn't have a turnable.

But my solutions concept is similar to yours:

Tilt the glass so that the water surface touches the rims of both the bottom and top circles. If it does, then its half.

Sorry for the clumsy explanation, its better to see it visually.

Title: Re: Easy: Glass half full
Post by jabhiji on Jan 30^th, 2003, 6:03am

Hmmm...Looks like I am thinking too hard. Your solution is much more simple and elegant.