Weights of $1\,g,2\,g.....,100\,g$ are suspended from the $1 \,cm, 2 \,cm, ...... 100\, cm, \,marks$ respectively of a light metre scale. Where should it be supported for the system to be in equilibrium ...... $cm$ mark.

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

The position vector of the centre of mass $\vec r\, cm$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

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

A uniform thin rod $AB$ of length $L$ has linear mass density $\mu \left( x \right) = a + \frac{{bx}}{L}$ , where $x$ is measured from $A$. If the $CM$ of the rod lies at a distance of $\left( {\frac{7}{12}} \right)L$ from $A$, then $a$ and $b$ are related as

$A$ small ball $B$ of mass $m$ is suspended with light inelastic string of length $L$ from $a$ block $A$ of same mass $m$ which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle $\theta$ from equilibrium position & then released. The displacement of centre of mass of $A+ B$ system till the string becomes vertical is