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System Of Particles And Rotational Motion

Question
CBSEENPH11020831

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of the disc with angular velocities ω1 and ω2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

  • 1 half straight I left parenthesis straight omega subscript 1 space plus straight omega subscript 2 right parenthesis squared
  • 1 fourth straight I left parenthesis straight omega subscript 1 space plus straight omega subscript 2 right parenthesis squared
  • straight I left parenthesis straight omega subscript 1 space plus straight omega subscript 2 right parenthesis squared
  • 1 over 8 straight I left parenthesis straight omega subscript 1 space plus straight omega subscript 2 right parenthesis squared

Solution

B.

1 fourth straight I left parenthesis straight omega subscript 1 space plus straight omega subscript 2 right parenthesis squared

C.

straight I left parenthesis straight omega subscript 1 space plus straight omega subscript 2 right parenthesis squared increment KE space equals space 1 half fraction numerator straight I subscript 1 straight I subscript 2 over denominator 2 straight I subscript 1 plus space straight I subscript 2 end fraction space left parenthesis straight omega subscript 1 space minus straight omega subscript 2 right parenthesis squared
equals space 1 half fraction numerator straight I squared over denominator left parenthesis 2 straight I right parenthesis end fraction left parenthesis straight omega subscript 1 minus straight omega subscript 2 right parenthesis squared
space equals 1 fourth straight I left parenthesis straight omega subscript 1 minus straight omega subscript 2 right parenthesis squared