Rotation 2 Question 20
20. 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 star $B$ about the centre of mass is
(2010)
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Answer:
Correct Answer: 20. (6)
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)
$$ \begin{array}{lr} =\frac{I _A}{I _B}+1=\frac{m _A r _A^{2}}{m _B r _B^{2}}+1=\frac{r _A}{r _B}+1 & \left(\text { as } m _A r _A=m _B r _B\right) \\ =\frac{11}{2.2}+1=6 & \text { as } r \propto \frac{1}{m} \end{array} $$
