Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

In a binary star system, two stars of masses \( m_1 \) and \( m_2 \) separated by distance \( d \) rotate in circular orbits around their common centre of mass under their mutual gravitational attraction. If \( r_1 \) and \( r_2 \) are the radii of their orbits and \( v_1 \) and \( v_2 \) are their respective orbital speeds, which of the following relations is correct?

1. A
   \( \frac{v_1}{v_2} = \frac{m_1}{m_2} \)
2. B
   \( \frac{v_1}{v_2} = \frac{m_2}{m_1} \)
3. C
   \( \frac{r_1}{r_2} = \frac{m_1}{m_2} \)
4. D
   \( \frac{v_1}{v_2} = \sqrt{\frac{m_2}{m_1}} \)