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Question

A binary star consists of two stars A (mass 2.2 M subscript s end subscript) and B (mass 11 M subscript s end subscript), where M subscript s end subscript 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

  1. 7  
  2. 6  
  3. 9  
  4. 10  

The correct answer is: 6


    fraction numerator L subscript T o t a l end subscript over denominator L subscript B end subscript end fraction equals fraction numerator left parenthesis I subscript A end subscript plus I subscript B end subscript right parenthesis omega over denominator I subscript B end subscript. omega end fraction (as omega will be same in both cases)
    equals fraction numerator I subscript A end subscript over denominator I subscript B end subscript end fraction plus 1 equals fraction numerator m subscript A end subscript r subscript A end subscript superscript 2 end superscript over denominator m subscript B end subscript r subscript B end subscript superscript 2 end superscript end fraction plus 1
    equals fraction numerator r subscript A end subscript over denominator r subscript B end subscript end fraction plus 1 (as m subscript A end subscript r subscript A end subscript equals m subscript B end subscript r subscript B end subscript right parenthesis
    equals fraction numerator 11 over denominator 2.2 end fraction plus 1 left parenthesis a s r proportional to fraction numerator 1 over denominator m end fraction right parenthesis
    equals 6
    therefore The correct answer is 6.

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