A binary star consists of two stars A (mass= 22 M _ s ) and B...

\dfrac{{\text{L}}_{\text{Total}}}{{\text{L}}_{\text{B}}} = \dfrac{\left({\text{I}}_{\text{A}} + {\text{I}}_{\text{B}}\right) \omega}{{\text{I}}_{\text{B}} \cdot \omega}$</p><p>(as$\omega$will be same in both cases)<br />$\dfrac{{\text{L}}_{\text{Total}}}{{\text{L}}_{\text{B}}} = \dfrac{{\text{I}}_{\text{A}}}{{\text{I}}_{\text{B}}} + 1 = \dfrac{{\text{m}}_{\text{A}}{\text{r}}_{\text{A}}^{2}}{{\text{m}}_{\text{B}}{\text{r}}_{\text{B}}^{2}} + 1$</p><p>\left({\text{as m}}_{\text{A}}{\text{r}}_{\text{A}} = {\text{m}}_{\text{B}}{\text{r}}_{\text{B}}\right)$

$\dfrac{{\text{L}}_{\text{Total}}}{{\text{L}}_{\text{B}}} = \dfrac{{m}_{B}}{{m}_{\text{A}}} + 1 = 0 . 5 + 1 = 1 . 5$