The moment of inertia of a thin uniform rectangular plate of mass ' $m$ ', having length ' $a$ ' and width '…

The moment of inertia of a thin uniform rectangular plate of mass ' $m$ ', having length ' $a$ ' and width ' $b$ ' about an axis perpendicular to the plane of the plate and passing through one of its vertices is
  1. $\frac{2}{3} \mathrm{mab}$
  2. $\frac{1}{3} \mathrm{mab}$
  3. $\frac{2}{3} \mathrm{~m}\left(\mathrm{a}^2+\mathrm{b}^2\right)$
  4. $\frac{1}{3} m\left(a^2+b^2\right)$

Solution


By parallel axes theorem. $\begin{aligned} & \mathrm{I}=\mathrm{I}_{\mathrm{cm}}+\mathrm{md}^2 \\ & =\frac{\mathrm{m}}{12}\left(\mathrm{a}^2+\mathrm{b}^2\right)+\mathrm{m}\left(\frac{\mathrm{a}^2+\mathrm{b}^2}{4}\right) \\ & =\frac{1}{3} \mathrm{~m}\left(\mathrm{a}^2+\mathrm{b}^2\right)\end{aligned}$

Asked in: AP EAMCET 2022 (08 Jul Shift 1)

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