WORTH READING 6 Mar 2006

A Great Mind

The following concerns a question in a physics degree exam at the
University
of Copenhagen.

"Describe how to determine the height of a skyscraper with a barometer."

One student replied:

"You tie a long piece of string to the neck of the barometer, and then
lower
the barometer from the roof of the skyscraper to the ground. The length
of
the string plus the length of the barometer will equal the height of the
building."

This highly original answer so incensed the examiner that the student
was
failed. The student appealed on the grounds that his answer was
indisputably
correct, and the university appointed an independent arbiter to decide
the
case. The arbiter judged that the answer was indeed correct, but did the
problem it was decided to call the student in and allow him six minutes
in
which to provide a verbal answer which showed at least a minimal
familiarity
with the basic principles of physics.

For five minutes the student sat in silence, forehead creased in
thought.
The arbiter reminded him that time was running out, to which the student
replied that he had several extremely relevant answers, but couldn't
make up
his mind which to use.

On being advised to hurry up the student replied as follows:

"Firstly, you could take the barometer up to the roof of the skyscraper,
drop it over the edge, and measure the time it takes to reach the
ground.
The height of the building can then be worked out from the formula H =
0.5g
x t squared. But bad luck on the barometer."

"Or if the sun is shining you could measure the height of the barometer,
then set it on end and measure the length of its shadow. Then you
measure
the length of the skyscraper's shadow, and thereafter it is a simple
matter
of proportional arithmetic to work out the height of the skyscraper."

"But if you wanted to be highly scientific about it, you could tie a
short
piece of string to the barometer and swing it like a pendulum, first at
ground level and then on the roof of the skyscraper. The height is
worked
out by the difference in the gravitational restoring force T = 2 pi
sqroot
(l / g)."

"Or if the skyscraper has an outside emergency staircase, it would be
easier
to walk up it and mark off the height of the skyscraper in barometer
lengths, then add them up."

"If you merely wanted to be boring and orthodox about it, of course, you
could use the barometer to measure the air pressure on the roof of the
skyscraper and on the ground, and convert the difference in millibars
into
feet to give the height of the building."

"But since we are constantly being exhorted to exercise independence of
mind
and apply scientific methods, undoubtedly the best way would be to knock
on
the janitor's door and say to him 'If you would like a nice new
barometer, I
will give you this one if you tell me the height of this skyscraper'."

The student was Niels Bohr. He gave us the structure of an Atom, for
which
he won the Nobel Prize in 1922.

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