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:

In the pulley system shown in the figure, the mass of $A$ is half of that of $\text{rod } B$. The rod length is $500 \text{ cm}$. The mass of pulleys and the threads may be neglected. The mass $A$ is set at the same level as the lower end of the rod and then released. After releasing the mass $A$, it would reach the top end of the rod $B$ in time (Assume $g=10 \text{ m/s}^2$): (in $\text{ s}$)

In the figure shown,the velocities of different blocks are given. The velocity of $C$ is ......... $m/s$.

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys as shown in the figure. Calculate the time taken by the box of mass $8\, {kg}$ to strike the ground starting from rest. (Use $g = 10\, {m/s^2}$) (in ${s}$)

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 $N-s$).

Calculate the acceleration of the block $B$ in the figure,assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and the pulleys and string are massless.