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, 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, since there was
no prohibition to use of string - as long as you pulled and did not push
with it - but did not display any clear knowledge of physics. To resolve 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 applicable 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 =
2pi Sq. root (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’.”
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The student was Niels Bohr, who later won the Nobel prize for Physics.
