Two blocks of same mass $(4\ kg)$ are placed according to diagram. Initial velocities of bodies are $4\ m/s$ and $2\ m/s$ and the string is taut. Find the impulse on $4\ kg$ when the string again becomes taut  .......... $N-s$

Two masses $M _{1}$ and $M _{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M _{2}$ is twice that of $M_{1}$. the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$. The acceleration of The system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be.

In the given figure acceleration of wedge $'A'$ is $10\ m/s^2$ along the inclined plane. (There is no friction between $A$ $\&$ $B$ and $A$ $\&$ fixed inclined plane.) Then acceleration of block $'B'$ will ............ $m/s^2$

If block $A$ is moving with an acceleration of $5\,m/s^2$, the acceleration of $B$ w.r.t. ground is

The pulleys in the diagram are all smooth and light. The acceleration of $A$ is a upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ is

A man of mass $60\ kg$ is standing on a platform of mass $40\ kg$ as shown in figure then what force man should apply on rope so that he accelerate up with the platform with acceleration of $2\ m/s^2$ ............ $N$