ENADE Física Practice Questions - ENADE Física - Exame Nacional De Desempenho Dos Estudantes Exam

Access More Questions

A two-body isolated gravitational system consists of masses $m_1$ and $m_2$ separated by distance $r$. Transforming the dynamics to the center-of-mass frame reduces the system to a single fictitious particle of reduced mass $\mu$ moving in central potential $V(r) = -\frac{G m_1 m_2}{r}$. What are the expressions for $\mu$ and total kinetic energy $T_{CM}$ in polar coordinates $(r, \theta)$?

$$\mu = \frac{m_1 m_2}{m_1 + m_2}$ and $T_{CM} = \frac{1}{2}\mu \dot{r}^2 + \frac{L^2}{2\mu r^2}$ $$\mu = \sqrt{m_1 m_2}$ and $T_{CM} = \frac{1}{2}\mu (\dot{r}^2 + r^2 \dot{\theta}^2)$ $$\mu = \frac{m_1 + m_2}{2}$ and $T_{CM} = \frac{1}{2}\mu \dot{r}^2 + \frac{L^2}{2(m_1+m_2) r^2}$ $$\mu = \frac{m_1 m_2}{m_1 + m_2}$ and $T_{CM} = \frac{1}{2}(m_1+m_2)\dot{r}^2 + \frac{L^2}{2\mu r^2}$

Correct Answer:

$$\mu = \frac{m_1 m_2}{m_1 + m_2}$ and $T_{CM} = \frac{1}{2}\mu \dot{r}^2 + \frac{L^2}{2\mu r^2}$

Access more questions from this quiz

Continue to ENADE Física Practice Questions - ENADE Física - Exame Nacional de Desempenho dos Estudantes Exam for more practice questions and the full quiz experience.

Access More Questions