Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

Three men $A, B$ and $C$ of masses $40\,kg, 50\,kg$ and $60\,kg$ are standing on a plank of mass $90\,kg$,which is kept on a smooth horizontal plane. If $A$ and $C$ exchange their positions,then mass $B$ will shift:

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 $100 \ m$)

$M$ mass of a man stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $\frac{M}{3}$,then the distance that the man moves relative to the ground is:

Two men $A$ and $B$ are standing on a plank. $B$ is at the middle of the plank and $A$ is at the left end of the plank. The bottom surface of the plank is smooth. The system is initially at rest and the masses are as shown in the figure. $A$ and $B$ start moving such that the position of $B$ remains fixed with respect to the ground and $A$ meets $B$. Then the point where $A$ meets $B$ is located at