For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $O$ (the centre of mass) and $O^{\prime}$ (corner point) is:
Correct Option: , 2
(2) Moment of inertia of rectangular sheet about an axis passing through $O$,
$I_{O}=\frac{M}{12}\left(a^{2}+b^{2}\right)=\frac{M}{12}\left[(80)^{2}+(60)^{2}\right]$
From the parallel axis theorem, moment of inertia about $O^{\prime}$,
$I_{O^{\prime}}=I_{O}+M(50)^{2}$
$\frac{I_{O}}{I_{O^{\prime}}}=\frac{\frac{M}{12}\left(80^{2}+60^{2}\right)}{\frac{M}{12}\left(80^{2}+60^{2}\right)+M(50)^{2}}=\frac{1}{4}$
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