Infinitely Many… Solutions!

Scientific rumors connect this story with Sir Ernest Rutherford, the “father” of nuclear physics. However, it is highly doubtful that Sir Rutherford, who at the time lived and worked in Canada, came to an exam of some unknown student in Denmark. In any case, the story is really curious and amusing…

Rutherford: “Once, a good friend of mine from Denmark asked me for an unexpected favor. He was a physics lecturer at the University of Copenhagen. He gave an F (a “Failing grade”) to one of his students. On the other hand, the student believed that he answered absolutely correctly, and demanded to give him an A (“Excellent grade”). Since my friend was a fair man, and the student was considered to be a very capable young man, a “Solomon’s judgment” style solution was proposed: the student should be examined by an independent person whose opinion is trusted by both sides. They chose me as an arbiter!

The question that caused the debate was: “How to measure height by means of a barometer?” The student suggested to tie the barometer to an end of a rope and gently lower it down until the barometer touches the ground, and then measure the length of the rope.

– The young man is right! – I thought, – But the answer has nothing to do with the material studied at the class, so my colleague is also right! What should I do?

I honestly shared my thoughts with the debaters, and suggested the student to give another answer. The student, almost without hesitation, proposed five more solutions:

  1. Drop the barometer from the highest peak of the object and measure the flight time. Using the formula h = (g*t ^ 2)/2, you can easily calculate the height.
  2. On a sunny day, measure the length of the barometer and the shadow cast by it, and then measure the shadow of the object whose height you want to measure. Using the equation of proportions, you can easily calculate the desired height.
  3. Tie a rope to the barometer, and using the barometer as a pendulum, determine the acceleration of gravity period of the pendulum’s oscillations on the ground and on the top of the object. Use the difference between the two to calculate the height of the object.
  4. Measure the length of the barometer, raising it evenly and count how many barometers can be consisted to fit the measured length (height).
  5. Promise to a person who knows the exact answer that you will give him the barometer if he shares the information about the object’s height.

When my colleague and I finished laughing, and my colleague proudly changed the grade to “Excellent”, I asked the student why he did that? I had no doubt that he had initially known the correct answer. The student replied that he tired already from the teachers at the gymnasium and the university, who were imposing a standard way of thinking on students. So, he decided to rebel. By the way, the name of this rebel was Niels Bohr…”

A barometer. Image by Wolfgang Eckert from Pixabay.

Featured image by Clker-Free-Vector-Images from Pixabay.

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