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Find the moment of inertia of a uniform ...

Find the moment of inertia of a uniform square plate of mass `M` and edge a about one of its diagonals.

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The correct Answer is:
A, B
Let small sectional area is at a distance d from xx' axils therefore mass at tehat small section `=m/a^2xxaxxdx`

Therefore moment of inertia about xx' axis
`I_(xx')=2int_0^(a/2) m/a^2xx(adx)xx x^2`
`=2xxm/a[x^3/3]_0^(a/2)`
`=2xxm/a[a^3/(3xx8)]=(ma^3)/12`
therefore, `I_(zz)=I_(xx)+I_(yy)`
`=2xx((ma^2)/12)=(ma^2)/6`
since the two diagoN/Als are perpendicular to each other therefore
`I_(zz)=I_(xx)+I_(yy)
`rarr (ma^2)/6=2xxI_(xx) (I_(xx)=I_(yy))`
`rarr I_(xx)=(ma^2)/12`
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