PhysicsA disc of mass ‘m’ and radius R has a concentric hole of radius ‘r’. Its M.I. about an axis through centre and normal to its plane is

A disc of mass ‘m’ and radius R has a concentric hole of radius ‘r’. Its M.I. about an axis through centre and normal to its plane is

  1. A

    m2(R-r)2

  2. B

    m2(R2-r2)

  3. C

    m2(R+r)2

  4. D

    m2(R2+r2)

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    Solution:

    solution

    The disc's moment of inertia when it has a hole

    Iο=12m1R2-12m2r2

    m1-m2=m______(1)

    also,

    m1R2, m2r2

    m1m2=R2r2______(2) 

    m11-r2R2=m

    m1=mR2R2-r2

    m2=mr2R2-r2

    Iο=m2(R2-r2)(R4-r4)=m2(R2+r2)

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