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KCET2018PhysicsRotational Motion

Moment of inertia of a body about two perpendicular axes ( X ) and ( Y ) in the plane of lamina are ( 20 Kg m² ) and ( 25 Kg m² ) respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of ( X ) and ( Y ) axes is

Options

  1. A( 5 Kg m² )
  2. B( 45 Kg m² )
  3. C( 12.5 Kg m² )
  4. D( 500 Kg m² )

Correct answer

B. ( 45 Kg m² )

Step-by-step solution

Given, moment of inertia of body about ( X ) axis ( I_ X =20 kgm ² ) Moment of inertia of body about ( Y ) axis ( =I_ Y =25 kgm ² ) Then by perpendicular axis theorem, moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia of two perpendicular axes through the same point. Therefore [ I_ Z =I_ X +I_ Y =(20+25) kgm ²=45 kgm ² ] Hence, moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of ( X ) and ( Y ) axes i

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