Two particles of masses $2 \ kg$ and $3 \ kg$ are moving along the $X$-axis with velocities $3 \ m/s$ and $2 \ m/s$ respectively. The velocity of the center of mass of this system is ........ $m/s$.

$A$ projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point,the projectile explodes into two parts of masses $M/4$ and $3M/4$ respectively. The heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from the point of firing) of the lighter part is .................. $km$.

$A$ balloon of mass $M$ with a light rope and a monkey of mass $m$ are at rest in mid-air. If the monkey climbs up the rope and reaches the top of the rope,the distance by which the balloon descends will be (Total length of the rope is $L$):

Two bodies of mass $4 \,kg$ and $5 \,kg$ are moving along east and north directions with velocities $5 \,m/s$ and $3 \,m/s$ respectively. The magnitude of the velocity of the centre of mass of the system is:

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If the distance covered by $m_1$ is $x$,then the distance covered by $m_2$ is:

Discuss the explosion of a projectile.