A Question In A Physics Degree Exam

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 immediately. 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 not display any noticeable 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 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 sqrroot (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, the only Dane to win the Nobel prize for
Physics.