Two blocks of same mass $4 \ kg$ are placed as shown in the diagram. The initial velocities of the blocks are $4 \ m/s$ (horizontal) and $2 \ m/s$ (downward). The string is initially taut. Find the impulse on the $4 \ kg$ block when the string again becomes taut (in $N-s$).

All surfaces shown in the figure are assumed to be frictionless, and the pulleys and the string are light. The acceleration of the block of mass $2 \,kg$ is:

If the blocks $A$ and $B$ are moving towards each other with accelerations $a$ and $b$ respectively,find the net acceleration of block $C$.

In the adjoining figure,if the acceleration of the wedge $M$ with respect to the ground is $a$,then:

$A$ frictionless cart $A$ of mass $100 \ kg$ carries two other frictionless carts $B$ and $C$ having masses $8 \ kg$ and $4 \ kg$ respectively,connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart $A$ so that the smaller carts do not move relative to it (in $N$)? (Take $g = 10 \ m/s^2$)

If the acceleration of block $A$ is $2\,m/s^2$ to the left and the acceleration of block $B$ is $1\,m/s^2$ to the left,then find the acceleration of block $C$.