Date: Tue May 06 2003 - 13:50:27 EDT

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On Tue, 6 May 2003, Gary Collins wrote:

> And in a similar vein,
>
> This is apparently one of Magnus Magnusson's favourite after-dinner stories, but originally came
> from the "Engineers Weekly" of Denmark, and illustrates the virtues - and pitfalls - of "thinking for
> oneself". It concerns the following question in a physics degree exam at the University of Copenhagen:
>
> "Describe how to determine the height of a skyscraper with a barometer."
>
> One enterprising 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
> verbally provide an 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 = 1/2gt
> squared (height equals half times gravity time 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 sqr root of l over 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 air
> pressure on the roof of the skyscraper, compare it with standard air pressure 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 unfortunate bit of this story is we never find out if the candidate in fact passed on the basis of this answer
> or was failed for being too cocky!

I don't know whether this is true or not, but in the version of this story
that I have heard, the student was Neils Bohr.

Gordon Brown
Department of Mathematics