*_How do you calculate the height of a sky scraper using a barometer ?_
*The following concerns a question in a physics degree exam at theUniversity of Copenhagen:
"Describe how to determine the height of a skyscraper with abarometer.
"One student replied:"You tie a long piece of string to the neck of the barometer, thenlower the barometer from the roof of the skyscraper to the ground. Thelength of the string plus the length of the barometer will equal theheight of the building."This highly original answer so incensed the examiner that thestudent was failed immediately.
He appealed on the grounds that hisanswer was indisputably correct, and the university appointed anindependent arbiter to decide the case. The arbiter judged that theanswer was indeed correct, but did not display any noticeable knowledgeof physics. To resolve the problem it was decided to call the student inand allow him six minutes in which to provide a verbal answer whichshowed at least a minimal familiarity with the basic principles ofphysics. For five minutes the student sat in silence, forehead creasedin thought. The arbiter reminded him that time was running out, to whichthe student replied that he had several extremely relevant answers, butcouldn't make up his mind which touse.
On being advised to hurry up the student replied as follows:
"Firstly, you could take the barometer up to the roof of theskyscraper, drop it over the edge, and measure the time it takes toreach the ground. The height of the building can then be worked out fromthe 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 thebarometer, then set it on end and measure the length of its shadow. Thenyou measure the length of the skyscraper's shadow, and thereafter it isa simple matter of proportional arithmetic to work uut the height of theskyscraper.
"But if you wanted to be highly scientific about it, you could tie ashort 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 heightis worked out by the difference in the gravitational restoring force T =2 pi sqrroot (l/g)."
Or if the skyscraper has an outside emergency staircase, it would beeasier to walk up it and mark off the height of the skyscraper inbarometer 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 ofthe skyscraper and on the ground, and convert the difference inmillibars into feet to give the height of the building.But since we are constantly being exhorted to exercise independenceof mind and apply scientific methods, undoubtedly the best way would beto knock on the janitor's door and say to him 'If you would like a nicenew barometer, I will give you this one if you tell me the height ofthis skyscraper'.
"The student was Niels Bohr, the only Dane to win the Nobel prize forPhysics.
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