What is the acceleration of block $B$ for the given system?

In each of the three arrangements,the block of mass $m_1$ is being pulled left with constant velocity $v$. There is no friction anywhere. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass $m_2$ in the three cases respectively is

For the given figure,find the speed of block $A$ when $\theta = 60^\circ$. The ring moves horizontally with a constant speed of $4 \, m/s$.

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 $\text{ s}$)

If the pulleys shown in the diagram are smooth and massless,and $a_1$ and $a_2$ are the accelerations of the blocks of mass $4 \, kg$ and $8 \, kg$ respectively,then:

$A$ 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.