USAAAO 2022, I кръг — Задача 5
USAAAO 2022 - First Round · 5 февруари 2022 г.
Условие
Two (spherical) asteroids, Ek and Do, are orbiting in free space around their stationary center of mass. Ek has mass and Do has mass , where is the mass of moon. What is the ratio of the angular momentum of the whole system to the angular momentum of Do about the center of mass of the system?
(a) 26
(b) 6
(c) 1.2
(d) 1.04
(e) 0.1667
Отговори
- C
Решение
If the distance between the asteroids is , then Ek would be distance from center of mass and would be at from center of mass. If Ek is orbiting with velocity . The orbital velocity of Do (as center of mass is stationary) would be . So, total angular momentum of system is , which is given by
While the angular momentum of Do is
So the required ratio is .
Answer: C
Оригинал в Архива: usaaao_first_exam_2022_problems.pdf · официални решения: usaaao_first_exam_2022_solutions-1.pdf