Question

What the ratio of masses? (b) The two stars of a double star system have concentric circular orbits of radii ri and r2. What is the ratio of their masses? Hint: The orbital speed v in a circular orbit of radius r is v rw, where w is the angular velocity.

Answer 1

Answer:

$\frac{m_1}{m_2} = \frac{r_2}{r_1}$

Explanation:

As we know that in dual mass system we have two masses moves in circular path such that they moves about their common center of mass

The mutual force on them will be centripetal force for both

$\frac{m_1v_1^2}{r_1} = \frac{m_2v_2^2}{r_2}$

also we know that

$v = r\omega$

$m_1\omega^2 r_1 = m_2\omega^2r_2$

since angular speed for both will be same

$\frac{m_1}{m_2} = \frac{r_2}{r_1}$