Question

A binary star consists of two stars A (mass $2.2M_s $ ) and B
(mass $1 M_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^2 _A}{ m_B r ^2 _B} +1 = \frac{r_A}{r_B}+1 \, \, \, \, \, \, \, \, (as m_A r_A = m_B r_B)$
$ \, \, \, \, \, \, \, \, \, \, \, = \frac{11}{2.2}+1 \, \, \, \, \, \, \, \, \, \bigg( as r \propto \frac{1}{m} \bigg) $
$ \, \, \, \, \, \, \, \, \, \, \, \, \, = 6 $
$\therefore $ The answer is 6.