Three masses are placed on the $x-$axis: $300 \, g$ at the origin,$500 \, g$ at $x = 40 \, cm$ and $400 \, g$ at $x = 70 \, cm$. The distance of the centre of mass from the origin is ....... $cm$.

Centre of mass $(C.M.)$ of three particles of masses $1 \,kg, 2 \,kg$ and $3 \,kg$ lies at the point $(1, 2, 3)$ and $C.M.$ of another system of particles of $3 \,kg$ and $2 \,kg$ lies at the point $(-1, 3, -2)$. Where should we put a particle of mass $5 \,kg$ so that the $C.M.$ of the entire system lies at the $C.M.$ of the first system?

The position vectors of two particles of masses $1 \ kg$ and $3 \ kg$ are $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$ respectively. The position vector of the center of mass of this system is:

The centre of mass of a triangle shown in the figure has coordinates

Find the center of mass $(x, y, z)$ of the following structure of four identical cubes if the length of each side of a cube is $1$ unit.

$A$ point object of mass $m$ is kept at $(a, 0)$ along the $x$-axis. What mass should be kept at $(-3a, 0)$ so that the center of mass lies at the origin?