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System Of Particles And Rotational Motion

Question
CBSEENPH11020415

A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω′

  • fraction numerator ωm over denominator left parenthesis straight m plus 2 straight M right parenthesis end fraction
  • fraction numerator straight omega space left parenthesis straight m space plus space 2 straight M right parenthesis over denominator straight m end fraction
  • fraction numerator straight omega space left parenthesis straight m minus 2 straight M right parenthesis over denominator left parenthesis straight m plus 2 straight M right parenthesis end fraction
  • fraction numerator ωm over denominator left parenthesis straight m plus straight M right parenthesis end fraction

Solution

A.

fraction numerator ωm over denominator left parenthesis straight m plus 2 straight M right parenthesis end fraction straight L subscript straight i space equals space straight L subscript straight f
mR squared straight omega space equals space left parenthesis mR squared space plus space 2 MR squared right parenthesis straight omega apostrophe
straight omega apostrophe space equals space open parentheses fraction numerator mω over denominator straight m plus 2 straight M end fraction close parentheses