## Fermi Questions

#### 2008 GCE A Level Physics Paper 1 Question 2

Which estimate is realistic?

A. The kinetic energy of a bus travelling on an expressway is 30 000 J.
B. The power of a domestic light is 300 W.
C. The temperature of a hot oven is 300 K.
D. The volume of air in a car tyre is 0.03 m3.

The answer to the above question is D.

Based on the assumption that the car type takes the shape of a cylinder with a circular hollow in the middle, and estimating the diameter of the wheel to be 60 cm, the diameter of the hub to be 40 cm and the width to be 20 cm, the volume can be calculated as below:

$V =\pi (r_2^2 - r_1^2)\times w= \pi (0.30^2 - 0.20^2)\times 0.20 = 0.031 m^3$

Almost every year, in the A level Physics paper 1, there will be a Fermi Question. A "Fermi question" is a question in physics which seeks a fast, rough estimate of quantity which is either difficult or impossible to measure directly. Also know as "back-of-the-envelope" questions, such questions could potentially stump the brightest students as well as the most hardworking ones.

Such questions are named after the American physicist Enrico Fermi. One example of him solving such a question was his estimate of the strength of the atomic bomb based on the distance travelled by bits of paper dropped from his hand at the test blasting.

Estimation in Physics uses simple numbers (usually 1, sometimes 2 or 5) with the correct order of magnitude (e.g. 103 or 10-4).

The answer calculated for the above MCQ does not have to be exactly the same as that in the option, just close enough.

The tip I would give my student for such questions will be to pay attention to the physical quantities around them. Values like the power rating of a fluorescent bulb (~10-20W), the mass of a bus (~10 tons), the speed limit on the expressway for a bus (60 km/h), the temperature of an oven (~200 degrees Celsius or ~473 K).