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 ${s}$)

If block $A$ is moving with an acceleration of $5\,m/s^2$,the acceleration of $B$ with respect to the ground is:

$A$ rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative.

The velocity of end $A$ of a rigid rod placed between two smooth perpendicular walls moves with velocity $u$ along the vertical direction. Find the velocity of end $B$ of the rod,given that the rod always remains in contact with the walls.

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 $\text{ s}$)

$A$ block $Q$ of mass $M$ is placed on a horizontal frictionless surface $AB$ and a body $P$ of mass $m$ is released on its frictionless slope. As $P$ slides by a length $L$ on this slope of inclination $\theta$,the block $Q$ would slide by a distance: