IIT-JEE 2010 · Paper 1 · Physics Q81

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PhysicsInteger+3Question 81 of 84

A binary star consists of two stars A (mass $2.2M_s$ ) and B (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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Answer and worked solution

Official answer: 6

Distances from the centre of mass. $m_Ar_A=m_Br_B$ , so $\dfrac{r_A}{r_B}=\dfrac{11}{2.2}=5$ .

Angular momenta (same $\omega$ ): $L=mr^2\omega$ , so
$\frac{L_A}{L_B}=\frac{m_A}{m_B}\left(\frac{r_A}{r_B}\right)^2=\frac15\times25=5.$

Ratio. $\dfrac{L_A+L_B}{L_B}=6$ .

Answer: 6

Topics:Angular momentum and its conservation Centre of mass

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IIT-JEE 2010 · Paper 1, Physics question 81