Physics - Rotation Question with Solution | TestHub

${\text{I}}_{\text{x}}={\text{I}}_{\text{y}}=2\left\{\frac{{\text{ml}}^2}{3}{\text{sin}}^{2}45^{\mathrm{o}}\right\}=\frac{{\text{ml}}^2}{3}$

${\text{I}}_{\text{z}}=2\left(\frac{{\text{ml}}^2}{3}\right)=\frac{2}{3}{\text{ml}}^2$

Hence,${\text{I}}_{\text{x}}={\text{I}}_{\text{y}}<{\text{I}}_{\text{z}}$

NOTE:for lx and ly you can remember the
following formula which is obtained by integration.

${\text{I}}_{\text{xx}}=\frac{{\text{ml}}^2}{3}{\text{sin}}^2\mathrm{\theta }$