Two blocks of masses $2 \,kg$ and $1 \,kg$ are tied to the ends of a string which passes over a light frictionless pulley. The blocks are held at rest at the same horizontal level and then released suddenly. The distance traversed by their centre of mass in $2 \,s$ is (acceleration due to gravity $g = 10 \,ms^{-2}$) (in $\,m$)

$A$ 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 .................. $km$.

$A$ system of two particles has masses $m_1$ and $m_2$. If the particle of mass $m_1$ is pushed towards the centre of mass of the particles through a distance $d$,by what distance should the particle of mass $m_2$ be moved to keep the centre of mass of the particles at the original position?

Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in the air,

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 objects of masses $200 \ g$ and $500 \ g$ have velocities $10\hat{i} \ m/s$ and $3\hat{i} + 5\hat{j} \ m/s$ respectively. The velocity of their center of mass (in $m/s$) is: