Question

A binary star consists of two stars A (mass $2.2M_s$ ) and B
(mass $1M_S$ ), where M s is the mass of the sun. They are
separated by distance d and are rotating about their centre of
mass, which is stationary. The ratio of the total angular
momentum of the binary star to the angular momentum of star
B about the centre of mass is

Answer 1

$\frac{L_{Total}}{L_B}$ ( as $\omega$will be same in both cases)
$=\frac{I_A}{I_B}+1=\frac{m_A{r}_A^2}{m_B{r}_B^2}+1=\frac{r_A}{r_B}+1(as{m}_A{r}_A=m_B{r}_B)$
$=\frac{11}{2.2}+1(asr\propto \frac{1}{m})$
$=6$
$\therefore$ The answer is 6.