$A$ 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

Seven identical homogeneous bricks, each of length $L$ , are arranged as shown in figure. Each brick is displaced with respect to the one in contacts by $\frac{L}{{10}}$ . Calculate the $x$-co-ordinate of the centre of mass of this system relative to the origin $O$ as shown 

Two particles of mass $5\, kg$ and $10\, kg$ respectively are attached to the two ends of a rigid rod of length $1\, m$ with negligible mass. The centre of mass of the system from the $5\, kg$ particle is nearly at a distance of $..........\, cm$

When does a body (system) have different centre of gravity and centre of mass ? 

A projectile of mass $3\,m$ explodes at highest point of its path. It breaks into three equal parts. One part retraces its path, the second one comes to rest. The distance of the third part from the point of projection when it finally lands on the ground is ........$m.$ (The range of the projectile was $100\,\,m$  if no explosion would have taken place)

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