The barometer question

I once heard Clement Freud tell this story on the wireless - and thought he said he was rector at the university in question. I came across it attributed to Niels Bohr, the Danish physicist, but that cannot be right since I hardly imagine there were many skyscrapers in Copenhagen when he was a student. The omniscient Wikipedia says it really happened, in the early 1960s in America, and that test designer Alexander Calandra wrote that he was the man called in to adjudicate on the student's appeal.

During a physics exam one day, a student was asked to "describe how to determine the height of a skyscraper with a barometer."

"You tie a long piece of string to the neck of the barometer," he replied, "and 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."

The student did not pass his exam. When he appealed, the university appointed an independent arbiter to decide the case. The arbiter concluded that the answer was correct but did not display any knowledge of physics. The student was called in and given six minutes to provide a proper answer.

For five minutes he sat in silence, thinking. When the arbiter reminded him that time was running out, the student replied that he had several solutions, but could not decide which to use. At last, he gave this reply:

"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.

"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 work out the height of the skyscraper using proportional arithmetic.

"You could also 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 sqroot (l / g).

"If you merely wanted to be boring and orthodox about it, 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 I think what I would really do would be to go down in the lift to the basement, find the caretaker and say to him, 'Look. This is a nice new barometer. I will give it to you, if you tell me the height of this building.'"