$A$ body falling vertically downwards under gravity breaks into two parts of unequal masses. The centre of mass of the two parts taken together

Two equal rods joined at one end are kept on a smooth surface as shown and released. The trajectory of the centre of mass of both rods is:

$A$ projectile of mass $3m$ explodes at its highest point into three equal fragments. One fragment returns to the point of projection. The second fragment comes to rest. The distance of the third fragment from the point of projection when it lands on the ground is ......... $m$. (The range of the projectile without explosion was $100 \ m$)

Two bodies of masses $M$ and $4M$ initially at rest,start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $v_0$ is

Two blocks of masses $10 \; kg$ and $30 \; kg$ are placed on the same straight line with coordinates $(0,0) \; cm$ and $(x, 0) \; cm$ respectively. The block of $10 \; kg$ is moved on the same line through a distance of $6 \; cm$ towards the other block. The distance through which the block of $30 \; kg$ must be moved to keep the position of the centre of mass of the system unchanged is

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of centre of mass of the system will be