At the university of Copenhagen, students were doing their physics degree exam. One of the questions came as follows: How to determine the height of a skyscraper using a barometer?

The correct answer, of course, is by measuring the difference in air pressure between the roof of the skyscraper and the ground. However, one of the students gave another answer:

“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."

On basis of such a provoking answer, the examiner decided to fail the student without further notice, despite the student insistence that his answer was correct. The university decided to appoint an independent arbiter to investigate this issue and come up with the decision on who is right and who wrong.

The arbiter judged that the answer was indeed correct, but that answer did not show any pre-knowledge relating to physics. Still, the arbiter decided that the student must be brought to him and demanded that the student has only 6 minutes to prove that he has the basis knowledge in Physics. The student sat down for 5 minutes, did not say anything, look like he was very deep with his thoughts. The arbiter warned the student that time was running out, but at that moment the student replied by saying that there are more than one answer for the question, but he did not make up his mind on which one to choose from, but when he was asked to hurry up he replied:

"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 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 sayto him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this building'."

The student was Niels Bohr (1885-1962), the only Dane to win the Nobel prize for Physics.

## Tuesday, October 17, 2006

### Lesson in Physics

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## 1 comment:

Thank you for an excellent story.

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