Moment of inertia of a circular wire of mass M and radius R about is its diameter is

Explanation

(i) Given Data: M = 500 g = 0.5 kg, `R = 10 cm = 10 xx 10^(-2) m`
`"Moment of inertia of disc about diameter" =Id=(1)/(4)MR^(2)`
`Id=(1)/(4) xx 0.5 xx 0.1 kg m^(2)`
(ii) Apply a parallel axes theorem, moment of inertia of the disc about a tangent to the disc and parallel to the diameter of the disc
`=(1)/(4)MR^(2)+MR^(2)=(5)/(4)MR^(2)=(5)/(4) xx 0.5 xx 0.1`
`=0.0625 kg m^(2)`
(iii) Moment of inertia of the disc about an axis passing through the centre of disc and perpendicular to the plane of the disc
`=(1)/(2)MR^(2)=(1)/(2) xx 0.5 xx 0.1=0.025 kg m^(2)`