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text  Two discs of moments of inertia  end text I subscript 1 text  and  end text I subscript 2 text  about their respective axes, rotating with angular  end text
text  frequencies,  end text omega subscript 1 text  and  end text omega subscript 2 text  respectively, are brought into contact face to face with their axes of  end text
text  rotation coincident. The angular frequency of the composite disc will be A  end text

  1. fraction numerator I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 over denominator I subscript 1 plus I subscript 2 end fraction
  2. fraction numerator I subscript 2 omega subscript 1 plus I subscript 1 omega subscript 2 over denominator I subscript 1 plus I subscript 2 end fraction
  3. fraction numerator I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 over denominator I subscript 1 minus I subscript 2 end fraction
  4. fraction numerator I subscript 2 omega subscript 1 plus I subscript 1 omega subscript 2 over denominator I subscript 1 minus I subscript 2 end fraction

The correct answer is: fraction numerator I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 over denominator I subscript 1 plus I subscript 2 end fraction


    L subscript i equals I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2
text  i.e.,  end text I equals I subscript 1 plus I subscript 2
L subscript f equals I omega equals open parentheses I subscript 1 plus I subscript 2 close parentheses omega
L subscript i equals L subscript f
I subscript i omega subscript 1 plus I subscript 2 omega subscript 2 equals open parentheses I subscript 1 plus I subscript 2 close parentheses omega
omega equals fraction numerator I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 over denominator I subscript 1 plus I subscript 2 end fraction

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