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Q.
A square plate of side $l$ has mass $M .$ What is its moment of inertia about one of its diagonals?
System of Particles and Rotational Motion
Solution:
Moment of inertia of a square about an axis through
its centre and perpendicular to its plane
$I_{O}=\frac{M}{12}\left(l^{2}+l^{2}\right)=\frac{M l^{2}}{6}$
According to theorem of perpendicular
axes, we get
$I_{1}+I_{2}=I_{O}=\frac{M l^{2}}{6}$
But $I_{1}=I_{2}$ (By symmetry)
$\therefore 2 I_{1}=\frac{M l^{2}}{6}$ or $I_{1}=\frac{M l^{2}}{12}$
