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  • For a uniform rectangular sheet shown in the figure, the ratio of moments of interia about the axes perpendicular to the sheet and

For a uniform rectangular sheet shown in the figure, the ratio of moments of interia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point ) is:
Option: 1 \frac{2}{3}
Option: 2 \frac{1}{4}
Option: 3 \frac{1}{8}
Option: 4 \frac{1}{2}

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\begin{array}{l} \mathrm{I}_{\mathrm{O}}=\frac{\mathrm{M}}{12}\left[\mathrm{~L}^{2}+\mathrm{B}^{2}\right]=\frac{\mathrm{M}}{12}\left[80^{2}+60^{2}\right] \\ \\ \mathrm{I}_{\mathrm{O}^{\prime}}=\mathrm{I}_{0}+\mathrm{Md}^{2}\{\text { parallel axis theorem } \\ \\ =\frac{\mathrm{M}}{12}\left[80^{2}+60^{2}\right]+\mathrm{M}[50]^{2} \\ \\ \frac{\mathrm{I}_{\mathrm{O}}}{\mathrm{I}_{\mathrm{O}}}=\frac{\mathrm{M} / 12\left[80^{2}+60^{2}\right]}{\frac{\mathrm{M}}{12}\left[80^{2}+60^{2}\right]+\mathrm{M}[50]^{2}}=\frac{1}{4} \end{array}

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Deependra Verma

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