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Q.

A binary star consists of two stars A (mass 2.2M_s), and B of mass (11M_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

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a

2

b

8

c

6

d

4

answer is C.

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Detailed Solution

we know that m₁d₁ = m₂d₂

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$∴ \frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1}} = \frac{11}{2.5} = 5$

d₁ = 5d₂ ........(i) d₁ + d₂ = d ....(ii)

$\Rightarrow d_{1} = \frac{5 d}{6} and d_{2} = \frac{d}{6}$

$\frac{L_{Binary}}{L_{B}} = \frac{11 m_{s} {(\frac{d}{6})}^{2} + 2.2 m_{s} {(\frac{5 d}{6})}^{2}}{11 m_{s} {(\frac{d}{6})}^{2}} = 6$

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A binary star consists of two stars A (mass 2.2Ms), and B of mass (11Ms) where Ms 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