PHYSICS EXAM

“Physics 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
using 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, 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 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 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’.”

The student was Niels Bohr, the only person from
Denmark to win the Nobel prize for Physics.

Niels Henrik David BOHR : (PLEASE CLICK)

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