A rod of length is $3 \mathrm{m}$ and its mass acting per unit length is directly proportional to distance, $x$ from one of its ends then its center of gravity from that end will be at: - 

The $ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}$ and $I_{CA}$ are the moments of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct ?

Three particles, each of mass $m$ gram, are situated at the vertices of an equilateral triangle $ABC$ of side $I \mathrm{cm}$ (as shown in the figure). The moment of inertia of the system about a line $AX$ perpendicular to $AB$ and in the plane of $ABC,$ in ${\mathrm{gcm}}^2$ units will be