USAPhO 2026, Първи кръг — Задача 7
2026 Exam · 1 т.
Указания
25 QUESTIONS - 75 MINUTES
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
- Use throughout, unless otherwise specified.
- You may write in this question booklet and the scratch paper provided by the proctor.
- This test has 25 multiple choice questions. Select the best response to each question, and use a No.2 pencil to completely fill the box corresponding to your choice. If you change an answer, completely erase the previous mark. Only use the boxes numbered 1 through 25 on the answer sheet.
- All questions are equally weighted, but are not necessarily equally difficult.
- You will receive one point for each correct answer, and zero points for each incorrect or blank answer. There is no additional penalty for incorrect answers.
- You may use a hand-held calculator. 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 external references, such as books or formula sheets.
- The question booklet, answer sheet and scratch paper will be collected at the end of this exam.
- To maintain exam security, do not communicate any information about the questions or their solutions until after February 13, 2026.
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
We acknowledge The US Physics Team coaches and other contributors to this year’s exams:
Tengiz Bibilashvili, Eddie Chen, Orhun Ciftcioglu, Kellan Colburn, Evan Erickson, Harry Kroft, Natalie LeBaron, Mai Qi, Elena Yudovina
Условие
The James Webb telescope lies at a point called the Lagrange Point 2 or L2. This is a point where the telescope would remain stationary in a frame rotating with Earth’s orbit around the sun, so a telescope placed exactly at L2 would be in an equilibrium position relative to Earth’s orbit. What is the stability of this equilibrium point with respect to radial and tangential perturbations?
(A) Stable to both radial and tangential perturbations.
(B) Stable to radial perturbations. Unstable to tangential perturbations.
(C) Stable to tangential perturbations. Unstable to radial perturbations.
(D) Unstable to both radial and tangential perturbations.
(E) None of the listed. L2 is not a real equilibrium point because the centrifugal force is a fictitious force.
Отговори
- C
Решение
Moving an object radially outwards will increase the centrifugal force and lower the gravitational force, so the point is unstable in the radial direction. The tangential force from Earth would increase faster than the tangential force from the centrifugal force, so the object experiences a restoring force tangentially.
Оригинал в Архива: 2026_FMA_exam.pdf · официални решения: 2026_FMA_solutions.pdf