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A binary star consists of two stars A (mass 2.2 M) and B (mass 11 M), The system rotates about its centre of mass which is stationary. The ratio of the total angular momentum of the system to the angular momentum of star B about the centre of mass is______

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answer is 6.

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Detailed Solution

$m_{A} x_{1} = m_{B} x_{2} \Rightarrow \frac{x_{1}}{x_{2}} = \frac{11}{2.2} = 5;$

$\begin{array}{l} L_{A} = m_{A} x_{1}^{2} ω \\ L_{B} = m_{B} x_{2}^{2} ω \end{array}$

$\Rightarrow \frac{\sum L}{L_{B}} = \frac{m_{A} x_{1}^{2} + m_{B} x_{2}^{2}}{m_{B} x_{2}^{2}} = 1 + \frac{m_{A}}{m_{B}} \times {(\frac{m_{B}}{m_{A}})}^{2} = 1 + 5 = 6$

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