INPhO 2022, Теория — Задача 2

Indian Olympiad Qualifier in Physics (IOQP) 2021-2022 — Part II: Indian National Physics Olympiad (INPhO) · 13 март 2022 г. · 10 т.

Указания

1. This booklet consists of 4 pages and total of 5 questions. Write roll number at the top wherever asked.

2. Booklet to write the answers is provided separately. Instructions to write the answers are on the Answer Booklet.

3. Marks will be awarded on the basis of what you write on both the Summary Answer Sheet and the Detailed Answer Sheets in the Answer Booklet. Simple short answers and plots may be directly entered in the Summary Answer Sheet. Marks may be deducted for absence of detailed work in questions involving longer calculations.

4. Strike out any rough work that you do not want to be considered for evaluation. You may also use the space on the Question Paper for rough work – this will NOT be evaluated.

5. Non-programmable scientific calculators are allowed. Mobile phones cannot be used as calculators.

6. Please submit the Answer Booklet at the end of the examination. You may retain the Question Paper.

Условие

The first explosion of an atomic bomb was the Trinity test in New Mexico in 1945. This explosion released a very large amount of energy $E$ which created an expanding fireball (known as the Trinity fireball). A snapshot of this fireball taken $0.025\,\mathrm{s}$ after the explosion is shown in the photograph below.

A scientist, Prof. Geoffrey Taylor, could make an estimate of the energy released by the bomb from an analysis of such photographs. Here we try to follow in his footsteps, with some suitable simplifications.

To begin, we assume that the fireball is spherical in nature. Its radius ($R$) increases with time ($t$) depending on the explosion energy $E$ and the density $\rho$ of the surrounding air (which is taken as constant and uniform).

We are also given a graph of the data obtained by Prof. Taylor, as shown below. However, the axes labels of the graph are missing.

Given data:

1 kiloton (kt) of TNT $= 4.2 \times 10^{12}\,\mathrm{J}$

Density $\rho$ of air outside the fireball $=1.22\,\mathrm{kg/m^3}$.

(a) What are the quantities represented by the axes of the graph? Also state the respective units in which they are expressed. In the detailed answer sheet, justify your answer. [3 т.]

(b) Find the slope ($s$) of the best fit line shown in the graph. What are the dimensions of the quantity $s$? [4 т.]

(c) From a dimensional analysis based on the above simplified model, make an estimate of the energy $E$ released (in kt of TNT) in the Trinity test. [3 т.]

Отговори

Решение

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Оригинал в Архива: IOQP2022-PartII-Questions-en.pdf · официални решения: IOQP2022-PartII-Solutions-20220503.pdf