Four holes of radius 5 cm are cut from a thin square plate of 20 cm...

Area mass density, \sigma=\frac{M}{16 R^2}\left(\because \text{ Area }=4 R $\times$4 R=16 R²\right) Mass$of each holem_1=\sigma \pi R^2=\frac{M}{16 R^2} \pi R^2=\frac{\pi M}{16}$ Distance between centre of plate and centre of hole x=$\frac{\sqrt{(2 R)^2+(2 R)^2}}{2}=\frac{2 \sqrt{2} R}{2} .<img src="/api/proxy-image?url=https$ \\ Moment of inertia of one hole at about Z-axis I_1=$\frac{1}{2}$m_1 R²+m_1 x²=$\frac{5 \pi}{32}$M R² Moment of inertia of whole plate about Z-axis, I=$\frac{M(4 R)^2}{6}=\frac{8}{3}$M R² Required moment of Inertia I_0=I-4 I_1,=\left[\frac{8}{3}-4\left(\frac{5 \pi}{32}\right)\right]$M R²=\left[\frac{8}{3}-\frac{5 \pi}{8}\right]$M R² Given, $R=5 \mathrm{~cm}$ and $M=1 \mathrm{~kg}$ So, $I_0=\left[\frac{8}{3}-\frac{5 \pi}{8}\right] 1 \times 25 \times 10^{-4}=0.0017 \mathrm{~kg}-\mathrm{m}^2$