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Question:

A binary star consists of two stars A (mass 2.2Ms) and B (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?

2

3

6

1

Solution:

Given M1=2.2Ms and M2=11Ms. Let R1 and R2 be their respective distances from the center of mass. The total angular momentum about the center of mass is LTotal=(I1+I2)ω and the angular momentum of B is L2=I2ω or LTotal/L2 = (I1+I2)/I2 = 1 + I1/I2 = 1 + M1R1^2/M2R2^2 = 1 + M1v1^2/M2v2^2 (as v=rω) = 1 + (M1v1/M2v2)^2 × M2/M1 = 1 + 1 × 11/2.2 = 6 (M1v1=M2v2)