A binary star consists of two stars A (mass 2.2 M_S ) and B (mass...

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 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

\operatorname{star} B

about the centre of mass is

Correct answer

Step-by-step solution

\frac{L_{\text{Total }}}{L_B}=\frac{\left(I_A+I_B\right) \omega}{I_B \cdot \omega}

(as

\omega

will be same in both cases)

\begin{aligned}& =\frac{I_A}{I_B}+1=\frac{m_A r_A^2}{m_B r_B^2}+1 \\ & \left.=\frac{r_A}{r_B}+1 \quad \quad \text{ (as }m_A r_A=m_B r_B\right) \\ & =\frac{11}{2.2}+1 \quad \quad\left(\text{ as })r \propto \frac{1}{m}\right)\\ & =6 \end{aligned}

\therefore

The correct answer is 6 .

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