If two bodies of masses $2 \,kg$ and $3 \,kg$ are moving at right angles with velocities $20 \,m \,s^{-1}$ and $10 \,m \,s^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is

Mention the position of the centre of mass of particles of equal mass.

An object comprises a uniform ring of radius $R$ and its uniform chord $AB$ (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object?

The centre of mass of three particles of masses $1 \ kg, 2 \ kg$ and $3 \ kg$ is at $(2, 2, 2)$. The position of the fourth mass of $4 \ kg$ to be placed in the system so that the new centre of mass is at $(0, 0, 0)$ is:

Four particles of masses $m_1 = 2m$,$m_2 = 4m$,$m_3 = m$,and $m_4$ are placed at the four corners of a square of side $a$. Let the corners be $(0,0)$,$(a,0)$,$(a,a)$,and $(0,a)$ respectively. What should be the value of $m_4$ so that the centre of mass of the system is at the centre of the square,i.e.,at $(\frac{a}{2}, \frac{a}{2})$?

$A$ system consists of $3$ particles each of mass $m$ located at $(1, 1), (2, 2),$ and $(3, 3)$. The coordinates of the centre of mass are