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KCET2015PhysicsMotion in One Dimension

Moment of Inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is ( I ). If the same rod is bent into a ring and its moment of inertia about its diameter is ( I^ ) then the ratio ( I I^ ) is

Options

  1. A( 3 2 ² )
  2. B( 8 3 ² )
  3. C( 2 3 ² )
  4. D( 5 3 ² )

Correct answer

C. ( 2 3 ² )

Step-by-step solution

Moment of inertia of a thin uniform rod is given as [ I= M L² 12 ] Moment of inertia of a ring is given as [ I^ = M R² 2 ] Therefore ( I I = ( M L² 12 ) ( M R² 2 ) = L² 6 R² ) Now, ( L=2 R ) Thus ( I I = (2 )² R² 6 R² = 4 ² 6 = 2 ² 3 )

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