USAPhO 2023, Първи кръг — Задача 19
2023 Exam · 1 т.
Указания
2023 Exam
25 QUESTIONS - 75 MINUTES
INSTRUCTIONS
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
- Use throughout this contest.
- You may write in this booklet of questions. However, you will not receive any credit for anything written in this booklet. You may only use the scratch paper provided by the proctor.
- This test contains 25 multiple choice questions. Select the answer that provides the best response to each question. Please be sure to use a No.2 pencil and completely fill the box corresponding to your choice. If you change an answer, the previous mark must be completely erased. Only the boxes preceded by numbers 1 through 25 are to be used on the answer sheet.
- All questions are equally weighted, but are not necessarily of the same level of difficulty.
- Correct answers will be awarded one point; incorrect answers or leaving an answer blank will be awarded zero points. There is no additional penalty for incorrect answers.
- A hand-held calculator may be used. Its memory must be cleared of data and programs. You may use only the basic functions found on a simple scientific calculator. Calculators may not be shared. Cell phones may not be used during the exam or while the exam papers are present. You may not use any tables, books, or collections of formulas.
- The question booklet, answer sheet and scratch paper will be collected at the end of this exam.
- In order to maintain exam security, do not communicate any information about the questions (or their answers or solutions) on this contest until after February 25, 2023.
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
We acknowledge the following people for their contributions to this year’s exams (in alphabetical order):
Tengiz Bibilashvili, Kellan Colburn, Samuel Gebretsadkan, Abi Krishnan, Natalie LeBaron, Kye Shi, Mike Winer, and Kevin Zhou
Условие
A student sets up a simple pendulum, measures its length to be , and observes a period of oscillation of . Using this data, the student computes . What is the uncertainty of this measurement?
- (A)
- (B)
- (C)
- (D)
- (E)
Отговори
- C
Решение
We have , and we can use the standard rules for propagation of relative uncertainties: the relative uncertainty of a product (or ratio) of two quantities adds in quadrature, and the relative uncertainty of a squared quantity is doubled. Thus,
which gives . (At the level of precision needed here, you could also note that is negligible, so we just have , which would give the same answer.) If one instead used
then the answer would instead be , which is not an answer choice. However, this is incorrect because independent relative uncertainties add in quadrature, rather than directly. For further details, see the solution to problem 12 of the 2018 exam A.
Оригинал в Архива: 2023_F-ma_Exam.pdf · официални решения: 2023_F-ma_Solutions_v3.pdf