Three point masses $m_1 = 1.6 \, kg$,$m_2 = 2.0 \, kg$,and $m_3 = 2.4 \, kg$ are placed at the corners of a thin massless rectangular sheet $(1.2 \, m \times 1.0 \, m)$ as shown. The center of mass will be located at the point ........... $m$.

Three particles of masses $50\, g$,$100\, g$,and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be

$A$ $T$-shaped object with dimensions shown in the figure is lying on a smooth floor. $A$ force $\vec{F}$ is applied at point $P$ parallel to $AB$,such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.

In the $HCl$ molecule,the separation between the nuclei of the two atoms is about $1.27 \; \mathring{A} \; (1 \; \mathring{A} = 10^{-10} \; m)$. Find the approximate location of the center of mass $(CM)$ of the molecule,given that a chlorine atom is about $35.5$ times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

The sum of moments of all the particles in a system about its center of mass is always . . . . . .

Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The magnitude of the position vector of the centre of mass of this system will be equal to the magnitude of which of the following vectors?