A Question of Physics

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 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 = 0.5 gt^2.
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
sqrt (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.

"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 mill bars into meters 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.