Fermi Estimation and Quick Measurement

An example of a scientist who could measure without instruments is Enrico Fermi (1901-1954), a physicist who won the Nobel Prize in physics in 1938. He had a well-developed knack for intuitive, even casual-sounding measurements. One renowned example of his measurement skills was demonstrated at the first detonation of the atom bomb, the Trinity Test site, on July 16, 1945, where he was one of the atomic scientists observing the blast from base camp. While final adjustments were being made to instruments used to measure the yield of the blast, Fermi was making confetti out of a page of notebook paper. As the wind from the initial blast wave began to blow through the camp, he slowly dribbled the confetti into the air, observing how far back it was scattered by the blast (taking the farthest scattered pieces as being the peak of the pressure wave). Fermi concluded that the yield must be greater than 10 kilotons. This would have been news since other initial observers of the blast did not know that lower limit. After much analysis of the instrument readings, the final yield estimate was determined to be 18.6 kilotons. Like Eratosthenes, Fermi was aware of a rule relating one simple observation—the scattering of confetti in the wind —to a quantity he wanted to measure.

The value of quick estimates was something Fermi was familiar with throughout his career. He was famous for teaching his students skills at approximation of fanciful-sounding quantities that, at first glance, they might presume they knew nothing about. The best-known example of such a "Fermi question" was Fermi asking his students to estimate the number of piano tuners in Chicago, when no one knows the answer. His students—science and engineering majors—would begin by saying that they could not possibly know anything about such a quantity. Of course, some solutions would be to simply do a count of every piano tuner perhaps by looking up advertisements, checking with a licensing agency of some sort, and so on But Fermi was trying to teach his students how to solve problems where the ability to confirm the results would not be so easy. He wanted them to figure out that they knew something about the quantity in question.

Suppose you apply the same logic as Fermi applied to confetti, which of the following statements would be the most appropriate?

Quick estimate, as per Fermi, is most useful in:

Given below are some statements that attempt to capture the central idea of the passage:

1. It is useful to estimate; even when the exact answer is known.
2. It is possible to estimate any physical quantity.
3. It is possible to estimate the number of units of a newly launched car that can be sold in a city.
4. Fermi was a genius.

Which of the following statements best captures the central idea?

Read the statements given below:

1. Atomic bomb detonation was a result of Fermi's Nobel Prize contribution
2. Fermi's students respected him as a scientist
3. Yield of atomic bomb can only be measured in Kilotons

Which of the following statement(s) can be inferred from the passage?