Two bodies of $6 \,kg$ and $4 \,kg$ masses have their velocities $5 \hat{i}-2 \hat{j}+10 \hat{k}$ and $10 \hat{i}-2 \hat{j}+5 \hat{k}$ respectively. Then the velocity of their centre of mass is

$A$ cart of mass $M$ is tied to one end of a massless rope of length $10\, m$. The other end of the rope is held by a man of mass $M$. The entire system is on a smooth horizontal surface. The man is at $x = 0$ and the cart is at $x = 10\, m$. If the man pulls the cart by the rope,the man and the cart will meet at the point:

Two particles of masses $m_1$ and $m_2$ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time $t$,when they are at a distance $r$ apart,is

Two masses of $1 \ kg$ and $2 \ kg$ are hanged from a pulley as shown in the figure. If the system starts from rest,find the distance travelled by the centre of mass in the first two seconds.

Two blocks $A$ and $B$ are joined together with a compressed spring. When the system is released,the two blocks move with unequal speeds in opposite directions as shown in the figure. Select the correct statement.

Discuss the explosion of a projectile.