Two point masses of mass $m_1=f M$ and $m_2=(1-f) M(f < 1)$ are in outer space (far from gravitational…
Two point masses of mass $m_1=f M$ 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
$(1-f) \omega_1=f \omega$
$\omega_1=\omega_2$ and independent of $f$
$f \omega_1=(1-f) \omega_2$
$\omega_1=\omega_2$ and depend on $f$
Solution
Angular velocity is the angular displacement per unit time i.e., $\omega=\frac{\Delta \theta}{\Delta t}$ Here $w_1=w_2$ and independent of $f$.