Two point masses of mass $$m_1 = fM$$ and $$m_2 = (1-f)M\ (f<1)$$ are in outer space (far from gravitational influence of other objects) at a distance $$R$$ from each other. They move in circular orbits about their centre of mass with angular velocities $$\omega_1$$ for $$m_1$$ and $$\omega_2$$ for $$m_2$$. In that case

A

$$(1-f)\omega_1 = f\omega$$

B

$$\omega_1 = \omega_2$$ and independent of $$f$$

C

$$f\omega_1 = (1-f)\omega_2$$

D

$$\omega_1 = \omega_2$$ and depend on $$f$$