USAAAO 2026, I кръг — Задача 19

USAAAO 2026 - First Round · 9 февруари 2026 г.

Problem writers

Problem writers: Srihari (Hari) Balaji, Vincent Bian, Ferdinand, Hagan Hensley, Elizabeth Lee, Joe McCarty, Lucas Pinheiro, Feodor Yevtushenko

Условие

Assume a spherical star has a density profile described by the equation below:

Find $\rho_c$ in terms of the total mass, $M$, and the radius of the star, $R$.

(a) $\frac{3M}{\pi R^3}$

(b) $\frac{15M}{8\pi R^3}$

(c) $\frac{3M}{2\pi R^3}$

(d) $\frac{21M}{16\pi R^3}$

(e) $\frac{6M}{5\pi R^3}$

Отговори

Решение

---

Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf