Q.
$ABC$ is a plane lamina of the shape of an equilateral triangle. $D,E$ are mid points of $AB,AC$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I_{0}.$ If part $ADE$ is removed, the moment of inertia of the remaining part about the same axis is $\frac{N I_{0}}{16}$ where $N$ is an integer. Value of $N$ is________.

NTA AbhyasNTA Abhyas 2022
Solution: