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?

In the figure,one-fourth part of a uniform disc of radius $R$ is shown. The distance of the centre of mass of this object from the centre $O$ is:

For determining the centre of mass of a body,why is a body considered as being composed of multiple small mass elements?

Center of mass of a system of three particles of masses $1 \, kg, 2 \, kg, 3 \, kg$ is at the point $(1 \, m, 2 \, m, 3 \, m)$ and center of mass of another group of two particles of masses $2 \, kg$ and $3 \, kg$ is at point $(-1 \, m, 3 \, m, -2 \, m)$. Where should a $5 \, kg$ particle be placed so that the center of mass of the system of all these six particles shifts to the center of mass of the first system?

$A$ particle of mass $m$ is moving in the $xy$-plane at a certain height from the ground along the $x$-axis. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. At that instant,the smaller fragment is at $y = 15 \ cm$. At this instant,the larger fragment will be at $y = $ ........ $cm$.

What do you mean by mass element $dm$?