A binary star consists of two stars A (mass 2.2 `M_(s)`) and B (mass 11 `M_(s)`), where `M_(s)` is the mass of the sun. They are separated by a 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.................... .

Explanation

Here distance of COM w.r.t. A
`=((11M_(S))/(11M_(S)+2.2M_(S)))xxd=(5d)/(6)`
`L_(A)=2.2M_(s)omega(5d//6)^(2)=55M_(s)omega((d^(2))/(36))`
`L_(B)=11M_(s)omega(d//6)^(2)=11M_(s)omega((d^(2))/(36))`
and `L_("total")=L_(A)+L_(B)=(11)/(6)M_(s)omegad^(2)`
`therefore (L_("total"))/(L_(B))=((11)/(6)M_(S)omegad^(2))/(11M_(S)omega(d//6)^(2))=6`