[Jokes4u] Determination of Height

[David Robinson]

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. He 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.

Alternatively, 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.

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).

If the skyscraper had 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.

However, 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.