What is the moment of inertia of the thin uniform rectangular plate of mass $m$ about the diagonal axis $x x^{'}$ ?

\frac{m (a^{2} + b^{2})}{24}

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\frac{m a^{2} b^{2}}{6 (a^{2} + b^{2})}

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\frac{m a^{2} b^{2}}{12 (a^{2} + b^{2})}

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\frac{m (a^{2} + b^{2})}{12}

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Solution

The correct option is B $\frac{m a^{2} b^{2}}{6 (a^{2} + b^{2})}$
M.I. of a angular section
$= 2 (M I o f t r i a n g l e p l a t e s a s s h o w n)$
$∵ \frac{r}{b} = \frac{b}{\sqrt{b^{2} + a^{2}}}$
$= \frac{1}{6} m {(\frac{a b}{\sqrt{a^{2} + b^{2}}})}^{2}$
$= \frac{1}{6} \frac{m a^{2} b^{2}}{(a^{2} + b^{2})}$

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What is the moment of inertia of the thin uniform rectangular plate of mass m about the diagonal axis xx′?

The correct option is B ma2b26(a2+b2)M.I. of a angular section=2(MIoftriangleplatesasshown) ∵rb=b√b2+a2=16m(ab√a2+b2)2=16ma2b2(a2+b2)

What is the moment of inertia of the thin uniform rectangular plate of mass $m$ about the diagonal axis $x x^{'}$ ?