Mass is distributed uniformly over a thin rectangular plate,and the positions of two vertices are given by $(1, 3)$ and $(2, -4)$. What is the position of the $3^{rd}$ vertex if the centre of mass of the plate lies at the origin?

Three masses of $2\,kg$,$4\,kg$,and $4\,kg$ are placed at the three points $(1, 0, 0)$,$(1, 1, 0)$,and $(0, 1, 0)$ respectively. The position vector of its center of mass is:

The distance between the carbon and oxygen atoms in a carbon monoxide molecule is $1.1 \, \mathring A$. Given that the mass of the carbon atom is $12 \, a.m.u.$ and the mass of the oxygen atom is $16 \, a.m.u.$,find the position of the center of mass of the carbon monoxide molecule.

Masses $8\,kg, 2\,kg, 4\,kg, 2\,kg$ are placed at the corners $A, B, C, D$ respectively of a square $ABCD$ of diagonal $80\,cm$. The distance of the centre of mass from $A$ will be ........ $cm$.

Three identical spheres,each of mass $M$,are placed at the corners of a right-angled triangle with mutually perpendicular sides equal to $2 \; m$ (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin,find the position vector of the center of mass.

For a body,the center of volume is defined as $\frac{\int \vec{r} \, dV}{\int dV}$ over the complete body,where $dV$ is a small volume element of the body and $\vec{r}$ is the position vector of that small volume from the origin. Which of the following statements is correct?